1. 2) Find one positive and one negative coterminal angle to 𝜋 3 .
Warm-up:
1) r = 9, θ = 230º
2) Find one positive and one negative coterminal angle to 𝜋 3 .
Find arc length S.
HW: Pg (2 – 30 even, 33, 37, 39, 41, 45, 47, 51)
Timed Five Minute Quiz on Unit Circle tomorrow!

2. a. I b.III a.III b. IV a. IV b. II a. IV b. III a. III b. II
HW Answers: p (5 – 10 , , 25, 27, 33 – 36 , 43 – 61 odd, 71, 73)
a. I b.III
a.III b. IV
a. IV b. II
a. IV b. III
a. III b. II
15) a. 25/12, -23/12 b. 8/3, -4/3
16) a. 19/6, -5/6 b. /6, -23/6
17) a. 7/4, - /4 b. 28/15, -32/15
18) a.26/9, -10/9 b. 98/45, -82/45
25) a. II b. IV
27) a. III b. I
33) a.405° , -315° b.324°, -396°
34) a.480°, -240 ° b. 330°, -30°
35) a. 660°, -60° b. 20°, -340°
36) a. 300°, -60° b. -130°, 590°
43) a. 270° b.210°
45) a. 420° b. -66°

3. HW Answers: p367-368 (5 – 10 , 15 -18 , 25, 27, 33 – 36 , 43 – 61 odd, 71, 73)
47) 2.007
49)
51) 9.285
53)
55) °
57) 337.5°
59) -756°
61) °
71) 6/5 rad
73) 32/7 rad

4. 4.2 Trigonometric Functions: The Unit circle
Objective:
Evaluate trigonometric functions
Use period to evaluate trigonometric functions
Evaluate trigonometric functions with a calculator.

5. The Unit Circle with Radian Measures

6. Do you remember 30º, 60º, 90º special right triangles?
long leg
hypotenuse
short leg
Hypotenuse = double the short leg
short leg = half the hypotenuse

7. The Unit Circle with Radian Measures
1 2 , 1
30o
60o
1/2
Hypotenuse = double the short leg
short leg = half the hypotenuse
long leg = short leg times

8. The Unit Circle with Radian Measures
− 1 2 ,
1 2 ,
− , 1 2
3 2 , 1 2
30o
60o 1
𝟏 𝟐
𝟑 𝟐
− , − 1 2
3 2 , − 1 2
− 1 2 ,−
1 2 ,−

9. Do you remember 45º, 45º, 90º isosceles right triangles?

10. The Unit Circle with Radian Measures
leg = hypotenuse times
45o 1
2 2 ,

11. The Unit Circle: Radian Measures and Coordinates
Trigonometric Functions:
Let t be a real number and let (x, y) be the point on the unit circle corresponding to t
sin t = y csc t = 1 𝑦
cos t = x sec t = 1 𝑥
tan t = 𝑦 𝑥 cot t = 𝑥 𝑦
(cos t, sin t)

12. Angles and the Unit Circle
Find the exact values of cos (–150°) and sin (–150°).
sin t = y csc t = 1 𝑦
cos t = x sec t = 1 𝑥
tan t = 𝑦 𝑥 cot t = 𝑥 𝑦
sin −150° =− 1 2
cos −150° =−

13. Find the six trig functions for 2𝜋 3
sin t = y csc t = 1 𝑦
cos t = x sec t = 1 𝑥
tan t = 𝑦 𝑥 cot t = 𝑥 𝑦
sin 2𝜋 3 =
cos 2𝜋 3 =− 1 2
tan 2𝜋 3 =
csc 2𝜋 3 =
sec 2𝜋 3 =
cot 2𝜋 3 =

14. Example:
Evaluate the six trigonometric functions of − 𝜋 4

15. Even and Odd Trig Functions:
Even: cos(-t) = cost
sec(-t) = sect
Odd: sin(-t) = -sint tan(-t) = -tant
csc(-t) = -csct cot(-t) = -cott

16. Using the Period to Evaluate Sine and Cosine:

17. Evaluating Trig Functions with a Calculator:
1) csc 𝜋 8 = 1 𝑠𝑖𝑛 𝜋 Mode: Radian
1  sin (   ENTER
Display: …
2) Sin 76.4 Mode: Degree
Sin ENTER
Display: …

18. Display: 0.0709… Evaluating Trig Functions with a Calculator:
2) cot 1.5 Mode: Radian
1  tan ( ENTER
Display: …

19. Evaluate the six trigonometric functions of − 9𝜋 4
Sneedlegrit:
Evaluate the six trigonometric functions of − 9𝜋 4
HW: Pg (2 – 30 even, 33, 37, 39, 41, 45, 47, 51)
Timed Five Minute Quiz on Unit Circle tomorrow!