Find the values of the six trigonometric functions for

Warm-Up: February 9, 2016

Homework Questions?

Trigonometric Functions of Any

AngleSection 4.4

We are no longer restricting ourselves to points on the unit circle.

Points can now be any distance “” away from the origin

Points are still always on the terminal side of θ. Initial side is still the positive -axis.

What’s New?

22 yxr

Name Abbreviation Relation to (x, y) and r

Restriction

Sine sin y/rCosine cos x/rTangent tan y/x x≠0Cosecant csc r/y y≠0Secant sec r/x x≠0Cotangent

cot x/y y≠0

The Six Trigonometric Functions

Let be a point on the terminal side of . Find each of the six trigonometric functions of .

Example 1

Let be a point on the terminal side of . Find each of the six trigonometric functions of .

You-Try #1

All Students Take Calculus

AS

T C

a) If and , in which quadrant does lie?b) If and , in which quadrant does lie?c) If and , in which quadrant does lie?

You-Try #3

Given that and , find the value of the rest of the trigonometric functions

Example 4

Given that and , find the value of the rest of the trigonometric functions

You-Try #4

Read Section 4.4 Page 474 #1-33 odd

Assignment

Given that and , find the value of the rest of the trigonometric functions

Warm-Up: February 10/11, 2016

Sections 4.1, 4.2, 4.4, and cofunctions from 4.3

20 questions◦ 8 multiple choice◦ 2 multiple response◦ 10 free response

No calculator You will get a blank unit circle with the test

◦ Filling it out is optional

Chapter 4A Test

Mr. Szwast is available most days during lunch in room 454 and after school in room 410.

Student tutors are available Mondays through Thursdays after school in room 410.

Edgenuity – you can sign up now for Chapter 4 A. Can be used to bring your test grade up to 70%.

www.khanacademy.org – instructional videos Interactmath.com – extra practice problems

aligned to our textbook

Need Help?

Homework Questions?

We like dealing with acute angles . We can often find trig functions of non-acute

angles by using an acute reference angle. Let be a non-acute angle in standard position

that lies in a quadrant (not on an axis) Its reference angle is the positive acute

angle formed by the terminal side of and the -axis

Reference Angles

For

Quadrant I:

Quadrant II:

Quadrant III:

Quadrant IV:

Finding the Reference Angle

360'180'

180''

Find the reference angle θ’ for each of the following angles:

You-Try #5

6)67)

120)160)

d

c

ba

1) Find the associated reference angle, 2) Find the trig function value of 3) Use the quadrant which lies in to choose

the appropriate sign to the value found in step 2

Using Reference Angles to Evaluate Trigonometric Functions

Find the exact value of each of the following:

Example 6

617sec)

225sin)240csc)47tan)

d

cb

a

Find the exact value of each of the following:

You-Try #6

4cot)

120tan)135cos)65sin)

d

cb

a

Trig Values Table

Read Section 4.4 Page 474 #1-33 odd Page 474 #35-65 Odd No calculators!

Assignment