Trigonometric Functions: The Unit Circle Section 4.2 Trigonometric Functions: The Unit Circle

Objective By following instructions students will be able to: Identify a unit circle and its relationship to real numbers. Evaluate trigonometric functions using the unit circle. Use the domain and period to evaluate sine and cosine functions. Evaluate trigonometric functions.

Unit Circle Circumference: Suppose radius=1 Then,

The Trigonometric Functions Let t be a real number and let (x,y) be the point on the unit circle corresponding to t.

Unit Circle

Example 1: Evaluating Trigonometric Functions a) b) c) d)

Example 2: Evaluating Trigonometric Functions Evaluate the six trigonometric functions at .

Domain and Period of Sine and Cosine? range Range Periodic Repeated revolutions or functions that behave in a repetitive manner.

Example 3: Use the Period to Evaluate Sine and Cosine a) b)

Trigonometric Functions Even and Odd Trigonometric Functions The cosine and secant functions are even. The sine, cosecant, tangent, and cotangent functions are odd.

Example 4: Using a Calculator a) b)

Revisit Objective Did we… Identify a unit circle and its relationship to real numbers? Evaluate trigonometric functions using the unit circle? Use the domain and period to evaluate sine and cosine functions? Evaluate trigonometric functions?

Homework Pg 300 #s 1-42 ALL