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Warm up….

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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Warm up….

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

  2. Section 4.2 THE UNIT CIRCLE

  3. 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 )

  4. A circle is symmetric with respect to? y = x Therefore, we can find other terminal points on this unit circle.

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

  6. Complete UNIT Circle

  7. 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:

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

  9. HW – DAY 1pg. 278 # 5 – 27 odd

  10. 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!!!

  11. Domains of Trig Functions

  12. Determining Signs of Trig Functions

  13. 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

  14. Some more practice evaluating: More practice…. Pg . 278 # 30 – 36 even

  15. HW DAY 2pg. 278 #’s 4, 6, 10, 14-28 even, 29-39 odd*Memorize Unit Circle and Trig Functions!!!!

  16. 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

  17. Some examples:

  18. 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!!

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

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