Chapter 44-4 Trigonometric functions at any angle

Objectives

•Students will know how to •evaluate trigonometric functions of any

angle,•Find reference angles •Evaluate trigonometric functions of real

numbers

Definition

Quadrants of circle

Example#1

•Name the quadrant in which lies if the cotangent is positive and the sine is negative.

Example#2

•Let (-3,4) be a point on the terminal side of

•Find sine, cosine, and tangent of

Example 3

•The point (-4, 10) is on the terminal side of an angle in standard position. Determine the exact values of the 6 trig functions.

Student guided practice

•Do problems 11-12 in your book page 289

Evaluating Trigonometric functions•Given sin=-2/3 and tan•Find cosine and cotangent

Example

•Given that cot =-4/3 and sin >0•Find the six trigonometric functions

Trigonometric functions of quadrant angles•Evaluate the cosine function and the

cotangent function•at the following four quadrant angles•A)

Student guided practice

•Do problems 29,30,39 in your book pagw 287 and 288

Reference angle

Reference angle

•reference angle: the acute angle formed by the terminal side of θ and the x-axis is called the reference angle

Example

•Find the reference angle for the following •A)

Student guided practice

•Do odd problems fro 47-51 page 290

Homework

•Do problems 13-17, 23,27,52 and 53 in your book page 289 and 290

Closure

•Today we learned about trigonometric functions at any angle

•Next we are going to see Graphs of sine and cosine