Lesson 2: 4.2 Trigonometric Functions: The Unit Circle

How do you evaluate trigonometric functions by using the unit circle?

unit circle
sine
cosine
tangent
cosecant
secant
cotangent
reciprocal
period

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.

Use Khan Academy resources.

Students will be introduced to the unit circle, the six trigonometric functions, and be able to evaluate sine and cosine functions using the domain and period.

Trigonometric functions are used to model the movement of an oscillating weight. For example, the displacement from equilibrium of an oscillating weight suspended by a spring is modeled as a function of time.

Some students incorrectly think that each trigonometric function is defined for every angle on the unit circle.
When calculating reciprocal functions on a calculator, some students may confuse reciprocal with inverse. Remind students to rewrite the expression in terms of sine, cosine, or tangent before evaluating.

Point out to students learning English that periodic is an adjective and that period is a noun. Explain that the most common definition of period is a unit of time. Discuss with students how the words period and periodic are related in common speech and how they are related in mathematical definitions.

Use common assessments.

Pre-Calculus with Limits resources.