#### T.1: The student, given a point other than the origin on the terminal side of an angle, will use the definitions of the six trigonometric functions to find the sine, cosine, tangent, cotangent, secant, and cosecant of the angle in standard position. Trigonometric functions defined on the unit circle will be related to trigonometric functions defined in right triangles.

Cosine Function

Sine Function

Tangent Function

#### T.2: The student, given the value of one trigonometric function, will find the values of the other trigonometric functions, using the definitions and properties of the trigonometric functions.

Sine, Cosine, and Tangent Ratios

#### T.3: The student will find, without the aid of a calculator, the values of the trigonometric functions of the special angles and their related angles as found in the unit circle. This will include converting angle measures from radians to degrees and vice versa.

Cosine Function

Sine Function

Tangent Function

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

Simplifying Trigonometric Expressions

Sum and Difference Identities for Sine and Cosine

#### T.6: The student, given one of the six trigonometric functions in standard form, will

T.6.b: determine the amplitude, period, phase shift, vertical shift, and asymptotes;

Cosine Function

Sine Function

Tangent Function

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

T.6.c: sketch the graph of the function by using transformations for at least a two-period interval; and

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

T.6.d: investigate the effect of changing the parameters in a trigonometric function on the graph of the function.

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

#### T.9: The student will identify, create, and solve real-world problems involving triangles. Techniques will include using the trigonometric functions, the Pythagorean Theorem, the Law of Sines, and the Law of Cosines.

Distance Formula

Pythagorean Theorem

Pythagorean Theorem with a Geoboard

Sine, Cosine, and Tangent Ratios

Correlation last revised: 9/16/2020