Warm up….Draw the special right triangles…

Find the side lengths for a triangle of hypotenuse 1:

√22

√22

√32

12

Section 4.2THE UNIT CIRCLE

The Unit Circle:The set of points at a distance 1 from the origin, a circle of radius 1

x2 + y2 = 1

Terminal Points: the point (x, y) from a distance around a circle starting from (1,0 )

Can you fill in the missing degree values and correct coordinates?

A circle is symmetric with respect to? y = x

Therefore, we can find other terminal points on this unit circle.

Complete UNIT Circle

Definition of the trigonometric functions:Let t be any real number and let P(x,y) be the

terminal point on the unit circle determined by t then:

Let’s practice finding the six trig functions when t = :

4

2

3

t

t

t

HW – DAY 1pg. 278 # 5 – 27 odd

4.2 – Day 2 Warm UpWithout using your notebook, calculator,

friends, etc. Fill out a blank unit circle.

If you talk or cheat you are disqualified!

*A correctly completed UNIT CIRCLE will

earn a 5 pt pass!!!

Domains of Trig Functions

Determining Signs of Trig Functions

When functions behave in a repetitive (or cyclic) manner, they are called PERIODIC.f( t + c) = f(t) “c” is the period…… try

to always use 2π

*this will help you evaluate numbers when they are not on the unit circle

(ex) Evaluate sin 13π 6

Some more practice evaluating:

More practice…. Pg . 278 # 30 – 36 even

HW DAY 2pg. 278 #’s 4, 6, 10, 14-28

even, 29-39 odd

*Memorize Unit Circle and Trig Functions!!!!

Even and Odd properties of Trig Functions:Even: Cosine and Secant

cos (-t) = cos (t) sec (-t)=sec (t)

Odd: sine, cosecant, tangent, and cotangent

sin (-t) = - sin t csc (-t) = -csc t

tan (-t) = - tan t cot (-t) = - cot t

Some examples:

Last but not least….Of course you can evaluate using your

calculator!!

The steps, if you don’t remember are on page 277 at the bottom!!

4.2 HW #2 (2015-16)pg. 278 #’s 4, 6, 10, 14-28 even, 29-39 oddPg. 278 #’s 43 – 52 all

Pg. 344 #’s 23 - 37 odd MEMORIZE UNIT CIRCLE AND TRIG FUNCTIONS!!

Some practice/HW – DAY 3Pg. 278 #’s 39 –

52 allPg. 344 #’s 23 -

37 odd MEMORIZE UNIT CIRCLE AND TRIG FUNCTIONS!!