M.O.T.3: Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships, specify locations and describe spatial relationships using coordinate geometry and other representational systems, apply transformations and use symmetry to analyze mathematical situations, and solve problems using visualization, spatial reasoning, and geometric modeling.

M.O.T.3.1: apply the right triangle definition of the six trigonometric functions of an angle to determine the values of the function values of an angle in standard position given a point on the terminal side of the angle.

M.O.T.3.1.b: using geometric principles and the Pythagorean Theorem, determine the six function values for the special angles and the quadrantal angles and use them in real-world problems.

Cosine Function
Sine Function
Tangent Function

M.O.T.3.3: using various methods, basic identities and graphical representation

M.O.T.3.3.a: verify trigonometric identities

Simplifying Trigonometric Expressions

M.O.T.3.5: find the value of the inverse trigonometric functions using special angle trigonometric function values and technology.

M.O.T.3.5.a: draw inferences of restricted domain to recognize and produce a graph of the inverse trigonometric functions.

Tangent Function

M.O.T.3.6: identify a real life problem utilizing graphs of trigonometric functions and/or the inverse functions; make a hypothesis as to the outcome; develop, justify, and implement a method to collect, organize, and analyze data; generalize the results to make a conclusion; compare the hypothesis and the conclusion; present the project using words, graphs, drawings, models, or tables.

Translating and Scaling Sine and Cosine Functions

M.O.T.3.8: investigate real-world problems within a project based investigation involving triangles using the trigonometric functions, the law of sines and the law of cosines, justify and present results.

Sine, Cosine, and Tangent Ratios

M.O.T.3.9: develop and test a hypothesis to find the area of a triangle given the measures of two sides and the included angle or the measures of three sides (Heron's formula) and use these formulas to find total area of figures constructed of multiple shapes.

Area of Triangles

M.O.T.3.10: express complex numbers in polar form:

M.O.T.3.10.a: perform operations including adding, subtracting, multiplying, and dividing;

Points in the Complex Plane

M.O.T.3.10.b: evaluate powers and roots of complex numbers using De Moivre's Theorem; and graph complex numbers.

Points in the Complex Plane
Roots of a Quadratic

M.O.T.3.10.c: graph complex numbers in the polar coordinate plane and make conjectures about some polar graphs and real-world situations such as the paths that the planets travel.

Points in the Complex Plane

M.O.T.3.11: create graphical and algebraic representations for performing vector operations and analyze these to solve real-world problems such as force analysis and navigation.

Adding Vectors
Vectors