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# Virginia - Mathematics: Trigonometry

## VA--Standards of Learning | Adopted: 2016

### TCTF: : Triangular and Circular Trigonometric Functions

TCTF.T.1: : The student, given a point on the terminal side of an angle in standard position, or the value of the trigonometric function of the angle, will determine the sine, cosine, tangent, cotangent, secant, and cosecant of 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

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

TCTF.T.2: : The student will develop and apply the properties of the unit circle in degrees and radians.

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

### GTF: : Graphs of Trigonometric Functions

GTF.T.3: : The student, given one of the six trigonometric functions in standard form, will

GTF.T.3.b: : determine the amplitude, period, phase shift, vertical shift, and asymptotes;

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

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

GTF.T.3.c: : sketch the graph of the function by using transformations for at least a two-period interval; and

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

GTF.T.3.d: : investigate the effect of changing the parameters in a trigonometric function on the graph of the function.

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

### EI: : Equations and Identities

EI.T.5: : The student will verify basic trigonometric identities and make substitutions, using the basic identities.

Simplifying Trigonometric Expressions

Choose the correct steps to simplify a trigonometric function. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview

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

EI.T.7: : The student will determine the value of any trigonometric function and inverse trigonometric function.

Cosine Function

Sine Function

Tangent Function

### ATF: : Applications of Trigonometric Functions

ATF.T.8: : The student will create and solve practical problems involving triangles.

Sine, Cosine, and Tangent Ratios

Reshape and resize a right triangle and examine how the sine of angle A, the cosine of angle A, and the tangent of angle A change. 5 Minute Preview

ATF.T.9: : The student will solve problems, including practical problems, involving

ATF.T.9.b: : linear and angular velocity.

Moment of Inertia

Place masses on a circular table and see how fast it spins when struck by a piston. Discover the relationships between angular velocity, mass, radius and moment of inertia for collections of point-masses, rings, disks, and more complex shapes. 5 Minute Preview

Correlation last revised: 9/16/2020

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