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# Common Core State Standards - Mathematics: High School: Functions

## Common Core State Standards | Adopted: 2010

### CCSS.Math.Content.HSF-IF: : Interpreting Functions

CCSS.Math.Content.HSF-IF.A: : Understand the concept of a function and use function notation

CCSS.Math.Content.HSF-IF.A.1: : Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

Introduction to Functions

Determine if a relation is a function using the mapping diagram, ordered pairs, or the graph of the relation. Drag arrows from the domain to the range, type in ordered pairs, or drag points to the graph to add inputs and outputs to the relation. 5 Minute Preview

Linear Functions

Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview

Points, Lines, and Equations

Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview

CCSS.Math.Content.HSF-IF.A.2: : Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

Absolute Value with Linear Functions

Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview

Exponential Functions

Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function. 5 Minute Preview

Points, Lines, and Equations

Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview

Quadratics in Polynomial Form

Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview

CCSS.Math.Content.HSF-IF.A.3: : Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

Arithmetic Sequences

Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response. 5 Minute Preview

Geometric Sequences

Explore geometric sequences by varying the initial term and the common ratio and examining the graph. Compute specific terms in the sequence using the explicit and recursive formulas. 5 Minute Preview

CCSS.Math.Content.HSF-IF.B: : Interpret functions that arise in applications in terms of the context

CCSS.Math.Content.HSF-IF.B.4: : For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

Absolute Value with Linear Functions

Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview

Exponential Functions

Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function. 5 Minute Preview

General Form of a Rational Function

Compare the equation of a rational function to its graph. Multiply or divide the numerator and denominator by linear factors and explore how the graph changes in response. 5 Minute Preview

Graphs of Polynomial Functions

Study the graphs of polynomials up to the fourth degree. Vary the coefficients of the equation and investigate how the graph changes in response. Explore things like intercepts, end behavior, and even near-zero behavior. 5 Minute Preview

Logarithmic Functions

Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes in response. Use the line *y* = *x* to compare the associated exponential function.
5 Minute Preview

Quadratics in Factored Form

Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response. 5 Minute Preview

Quadratics in Polynomial Form

Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview

Quadratics in Vertex Form

Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response. 5 Minute Preview

Radical Functions

Compare the graph of a radical function to its equation. Vary the terms of the equation. Explore how the graph is translated and stretched by the changes to the equation. 5 Minute Preview

Slope-Intercept Form of a Line

Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview

Standard Form of a Line

Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview

CCSS.Math.Content.HSF-IF.B.5: : Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

Absolute Value with Linear Functions

Compare the graph of a linear function, the graph of an absolute-value function, and the graphs of their translations. Vary the coefficients and constants in the functions and investigate how the graphs change in response. 5 Minute Preview

Exponential Growth and Decay

Explore the graph of the exponential growth or decay function. Vary the initial amount and the rate of growth or decay and investigate the changes to the graph. 5 Minute Preview

Points, Lines, and Equations

Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview

CCSS.Math.Content.HSF-IF.B.6: : Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

Distance-Time Graphs

Create a graph of a runner's position versus time and watch the runner complete a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the speed of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. 5 Minute Preview

Distance-Time Graphs - Metric

Create a graph of a runner's position versus time and watch the runner complete a 40-meter dash based on the graph you made. Notice the connection between the slope of the line and the speed of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. 5 Minute Preview

Distance-Time and Velocity-Time Graphs

Create a graph of a runner's position versus time and watch the runner run a 40-yard dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time. 5 Minute Preview

Distance-Time and Velocity-Time Graphs - Metric

Create a graph of a runner's position versus time and watch the runner run a 40-meter dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time. 5 Minute Preview

Slope

Explore the slope of a line, and learn how to calculate slope. Adjust the line by moving points that are on the line, and see how its slope changes. 5 Minute Preview

CCSS.Math.Content.HSF-IF.C: : Analyze functions using different representations

CCSS.Math.Content.HSF-IF.C.7: : Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

CCSS.Math.Content.HSF-IF.C.7.a: : Graph linear and quadratic functions and show intercepts, maxima, and minima.

Point-Slope Form of a Line

Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview

Quadratics in Factored Form

Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response. 5 Minute Preview

Quadratics in Polynomial Form

Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response. 5 Minute Preview

Quadratics in Vertex Form

Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response. 5 Minute Preview

Roots of a Quadratic

Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane. 5 Minute Preview

Slope-Intercept Form of a Line

Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview

Standard Form of a Line

Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview

Translating and Scaling Functions

Vary the coefficients in the equation of a function and examine how the graph of the function is translated or scaled. Select different functions to translate and scale, and determine what they have in common. 5 Minute Preview

CCSS.Math.Content.HSF-IF.C.7.b: : Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

Absolute Value with Linear Functions

Radical Functions

Compare the graph of a radical function to its equation. Vary the terms of the equation. Explore how the graph is translated and stretched by the changes to the equation. 5 Minute Preview

Translating and Scaling Functions

Vary the coefficients in the equation of a function and examine how the graph of the function is translated or scaled. Select different functions to translate and scale, and determine what they have in common. 5 Minute Preview

CCSS.Math.Content.HSF-IF.C.7.c: : Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

Graphs of Polynomial Functions

Study the graphs of polynomials up to the fourth degree. Vary the coefficients of the equation and investigate how the graph changes in response. Explore things like intercepts, end behavior, and even near-zero behavior. 5 Minute Preview

Polynomials and Linear Factors

Create a polynomial as a product of linear factors. Vary the values in the linear factors to see how their connection to the roots of the function. 5 Minute Preview

CCSS.Math.Content.HSF-IF.C.7.d: : Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

General Form of a Rational Function

Compare the equation of a rational function to its graph. Multiply or divide the numerator and denominator by linear factors and explore how the graph changes in response. 5 Minute Preview

Rational Functions

Compare the graph of a rational function to its equation. Vary the terms of the equation and explore how the graph is translated and stretched as a result. Examine the domain on a number line and compare it to the graph of the equation. 5 Minute Preview

CCSS.Math.Content.HSF-IF.C.7.e: : Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

Exponential Functions

Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function. 5 Minute Preview

Introduction to Exponential Functions

Explore the graph of the exponential function. Vary the initial amount and base of the function. Investigate the changes to the graph. 5 Minute Preview

Logarithmic Functions

Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes in response. Use the line *y* = *x* to compare the associated exponential function.
5 Minute Preview

Logarithmic Functions: Translating and Scaling

Vary the values in the equation of a logarithmic function and examine how the graph is translated or scaled. Connect these transformations with the domain of the function, and the asymptote in the graph. 5 Minute Preview

Translating and Scaling Functions

Vary the coefficients in the equation of a function and examine how the graph of the function is translated or scaled. Select different functions to translate and scale, and determine what they have in common. 5 Minute Preview

CCSS.Math.Content.HSF-IF.C.8: : Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

CCSS.Math.Content.HSF-IF.C.8.a: : Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

Quadratics in Factored Form

Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response. 5 Minute Preview

CCSS.Math.Content.HSF-IF.C.8.b: : Use the properties of exponents to interpret expressions for exponential functions.

Compound Interest

Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview

Exponential Growth and Decay

Explore the graph of the exponential growth or decay function. Vary the initial amount and the rate of growth or decay and investigate the changes to the graph. 5 Minute Preview

### CCSS.Math.Content.HSF-BF: : Building Functions

CCSS.Math.Content.HSF-BF.A: : Build a function that models a relationship between two quantities

CCSS.Math.Content.HSF-BF.A.1: : Write a function that describes a relationship between two quantities.

CCSS.Math.Content.HSF-BF.A.1.a: : Determine an explicit expression, a recursive process, or steps for calculation from a context.

Arithmetic Sequences

Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response. 5 Minute Preview

Arithmetic and Geometric Sequences

Find the value of individual terms in an arithmetic or geometric sequence using graphs of the sequence and direct computation. Vary the common difference and common ratio and examine how the sequence changes in response. 5 Minute Preview

Geometric Sequences

Explore geometric sequences by varying the initial term and the common ratio and examining the graph. Compute specific terms in the sequence using the explicit and recursive formulas. 5 Minute Preview

CCSS.Math.Content.HSF-BF.A.1.b: : Combine standard function types using arithmetic operations.

Addition and Subtraction of Functions

Explore the graphs of two polynomials and the graph of their sum or difference. Vary the coefficients in the polynomials and investigate how the graphs change in response. 5 Minute Preview

CCSS.Math.Content.HSF-BF.A.2: : Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

Arithmetic Sequences

Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response. 5 Minute Preview

Arithmetic and Geometric Sequences

Find the value of individual terms in an arithmetic or geometric sequence using graphs of the sequence and direct computation. Vary the common difference and common ratio and examine how the sequence changes in response. 5 Minute Preview

Geometric Sequences

Explore geometric sequences by varying the initial term and the common ratio and examining the graph. Compute specific terms in the sequence using the explicit and recursive formulas. 5 Minute Preview

CCSS.Math.Content.HSF-BF.B: : Build new functions from existing functions

CCSS.Math.Content.HSF-BF.B.3: : Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

Exponential Functions

Graphs of Polynomial Functions

Study the graphs of polynomials up to the fourth degree. Vary the coefficients of the equation and investigate how the graph changes in response. Explore things like intercepts, end behavior, and even near-zero behavior. 5 Minute Preview

Introduction to Exponential Functions

Explore the graph of the exponential function. Vary the initial amount and base of the function. Investigate the changes to the graph. 5 Minute Preview

Logarithmic Functions: Translating and Scaling

Vary the values in the equation of a logarithmic function and examine how the graph is translated or scaled. Connect these transformations with the domain of the function, and the asymptote in the graph. 5 Minute Preview

Quadratics in Polynomial Form

Quadratics in Vertex Form

Compare the graph of a quadratic to its equation in vertex form. Vary the terms of the equation and explore how the graph changes in response. 5 Minute Preview

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

Experiment with the graph of a sine or cosine function. Explore how changing the values in the equation can translate or scale the graph of the function. 5 Minute Preview

Zap It! Game

Adjust the values in a quadratic function, in vertex form or in polynomial form, to "zap" as many data points as possible. 5 Minute Preview

CCSS.Math.Content.HSF-BF.B.4: : Find inverse functions.

CCSS.Math.Content.HSF-BF.B.4.a: : Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse.

Logarithmic Functions

Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes in response. Use the line *y* = *x* to compare the associated exponential function.
5 Minute Preview

Radical Functions

Compare the graph of a radical function to its equation. Vary the terms of the equation. Explore how the graph is translated and stretched by the changes to the equation. 5 Minute Preview

CCSS.Math.Content.HSF-BF.B.4.c: : Read values of an inverse function from a graph or a table, given that the function has an inverse.

Logarithmic Functions

*y* = *x* to compare the associated exponential function.
5 Minute Preview

CCSS.Math.Content.HSF-BF.B.5: : Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

Logarithmic Functions

*y* = *x* to compare the associated exponential function.
5 Minute Preview

### CCSS.Math.Content.HSF-LE: : Linear, Quadratic, and Exponential Models

CCSS.Math.Content.HSF-LE.A: : Construct and compare linear, quadratic, and exponential models and solve problems

CCSS.Math.Content.HSF-LE.A.1: : Distinguish between situations that can be modeled with linear functions and with exponential functions.

CCSS.Math.Content.HSF-LE.A.1.a: : Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

Arithmetic and Geometric Sequences

Find the value of individual terms in an arithmetic or geometric sequence using graphs of the sequence and direct computation. Vary the common difference and common ratio and examine how the sequence changes in response. 5 Minute Preview

CCSS.Math.Content.HSF-LE.A.1.b: : Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

Arithmetic Sequences

Arithmetic and Geometric Sequences

CCSS.Math.Content.HSF-LE.A.1.c: : Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

Arithmetic and Geometric Sequences

Compound Interest

Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview

Exponential Growth and Decay

Explore the graph of the exponential growth or decay function. Vary the initial amount and the rate of growth or decay and investigate the changes to the graph. 5 Minute Preview

Geometric Sequences

CCSS.Math.Content.HSF-LE.A.2: : Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

Arithmetic Sequences

Arithmetic and Geometric Sequences

Compound Interest

Explore compound interest in-depth, from compounded annually to compounded continuously. In addition, compare the END POINTS graph, with dots that fit an exponential curve, to the ALL TIME graph, which has a more step-like appearance. 5 Minute Preview

Exponential Functions

Exponential Growth and Decay

Geometric Sequences

Introduction to Exponential Functions

Explore the graph of the exponential function. Vary the initial amount and base of the function. Investigate the changes to the graph. 5 Minute Preview

Point-Slope Form of a Line

Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview

Slope-Intercept Form of a Line

Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview

Standard Form of a Line

Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview

CCSS.Math.Content.HSF-LE.A.3: : Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

Arithmetic and Geometric Sequences

CCSS.Math.Content.HSF-LE.A.4: : For exponential models, express as a logarithm the solution to (ab)^(ct) = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

Logarithmic Functions

*y* = *x* to compare the associated exponential function.
5 Minute Preview

CCSS.Math.Content.HSF-LE.B: : Interpret expressions for functions in terms of the situation they model

CCSS.Math.Content.HSF-LE.B.5: : Interpret the parameters in a linear or exponential function in terms of a context.

Compound Interest

Exponential Growth and Decay

Slope-Intercept Form of a Line

Standard Form of a Line

### CCSS.Math.Content.HSF-TF: : Trigonometric Functions

CCSS.Math.Content.HSF-TF.A: : Extend the domain of trigonometric functions using the unit circle

CCSS.Math.Content.HSF-TF.A.1: : Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

Cosine Function

Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle. 5 Minute Preview

Radians

As factory belt operator, your job is to move boxes just the right distance on the belt, so they can be stamped for delivery. Your only controls are the radius and rotation of the belt’s wheel. How do you set these to get the distance right? See how this relates to arc length, and discover how radians help make this task easier. 5 Minute Preview

Sine Function

Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle. 5 Minute Preview

Tangent Function

Compare the graph of the tangent function with the graph of the angle on the unit circle. Drag a point along the tangent curve and see the corresponding angle on the unit circle. 5 Minute Preview

CCSS.Math.Content.HSF-TF.A.2: : Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

Cosine Function

Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle. 5 Minute Preview

Sine Function

Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle. 5 Minute Preview

Tangent Function

Compare the graph of the tangent function with the graph of the angle on the unit circle. Drag a point along the tangent curve and see the corresponding angle on the unit circle. 5 Minute Preview

CCSS.Math.Content.HSF-TF.A.3: : Use special triangles to determine geometrically the values of sine, cosine, tangent for pi/3, pi/4 and pi/6, and use the unit circle to express the values of sine, cosine, and tangent for pi – x, pi + x, and 2pi – x in terms of their values for x, where x is any real number.

Cosine Function

Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle. 5 Minute Preview

Sine Function

Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle. 5 Minute Preview

Tangent Function

Compare the graph of the tangent function with the graph of the angle on the unit circle. Drag a point along the tangent curve and see the corresponding angle on the unit circle. 5 Minute Preview

CCSS.Math.Content.HSF-TF.A.4: : Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

Cosine Function

Sine Function

Tangent Function

CCSS.Math.Content.HSF-TF.B: : Model periodic phenomena with trigonometric functions

CCSS.Math.Content.HSF-TF.B.5: : Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

Sine Function

Sound Beats and Sine Waves

Listen to and see interference patterns produced by sound waves with similar frequencies. Test your ability to distinguish and match sounds as musicians do when they tune their instruments. Calculate the number of "sound beats" you will hear based on the frequency of each sound. [Note: Headphones are recommended for this Gizmo.] 5 Minute Preview

Translating and Scaling Sine and Cosine Functions

Experiment with the graph of a sine or cosine function. Explore how changing the values in the equation can translate or scale the graph of the function. 5 Minute Preview

Waves

Observe and measure transverse, longitudinal, and combined waves on a model of a spring moved by a hand. Adjust the amplitude and frequency of the hand, and the tension and density of the spring. The speed and power of the waves is reported, and the wavelength and amplitude can be measured. 5 Minute Preview

CCSS.Math.Content.HSF-TF.C: : Prove and apply trigonometric identities

CCSS.Math.Content.HSF-TF.C.8: : Prove the Pythagorean identity sin²(theta) + cos²(theta) = 1 and use it to find sin(theta), cos(theta), or tan(theta) given sin(theta), cos(theta), or tan(theta) and the quadrant of the angle.

Cosine Function

Sine Function

CCSS.Math.Content.HSF-TF.C.9: : Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

Sum and Difference Identities for Sine and Cosine

Choose the correct steps to evaluate a trigonometric expression using sum and difference identities. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview

Correlation last revised: 7/7/2022

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