Warm up….

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# Warm up…. - PowerPoint PPT Presentation

Warm up…. Draw the special right triangles… Find the side lengths for a triangle of radius 1:. Section 4.2 THE UNIT CIRCLE. The Unit Circle:. The set of points at a distance 1 from the origin, a circle of radius 1. x 2 + y 2 = 1.

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Presentation Transcript
Warm up….
• Draw the special right triangles…
• Find the side lengths for a triangle of radius 1:

Section 4.2

THE 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 )

A circle is symmetric with respect to?

y = x

Therefore, we can find other terminal points on this 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:
4.2 – Day 2 Warm Up
• Without 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!!!

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

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!!

Some practice/HW – DAY 3
• Pg. 278 #’s 39 – 52 all, 53, 55, and 58