HW 9

P 56-58 (19-21, 42-50 even,

56, 57, 66, 68-72 even)

P100 (12-22 even, 19)

19 Find the angles of smallest possible measure coterminal with the following angles: -51 (Like #2)

y

x

5

5

-5-5

19 Find the angles of smallest possible measure coterminal with the following angles: -51 (Like #2)

360°

-51°

309°

y

x

5

5

-5-5

20 Find the angles of smallest possible measure coterminal with the following angles: -174 (Like #2)

y

x

5

5

-5-5

20 Find the angles of smallest possible measure coterminal with the following angles: -174 (Like #2)

360°

-174 186°

y

x

5

5

-5-5

21 Find the angles of smallest possible measure coterminal with the following angles: 792 (Like #1)

y

x

5

5

-5-5

21 Find the angles of smallest possible measure coterminal with the following angles: 792 (Like #1)

792 – 720 72

y

x

5

5

-5-5

72.If for , sin < 0 and cos > 0, in what quadrant must lie? What is the sign of tan ? (Like # 3-8)

sin < 0 and cos > 0

tan is ___________in Quadrant lV.

72.If for , sin < 0 and cos > 0, in what quadrant must lie? What is the sign of tan ? (Like # 3-8)

sin < 0 and cos > 0

lll, lV l, lV

lV

tan is negative in Quadrant lV.

44 Find the values of the six trigonometric functions for an angle of 360. (Like #9-12)(R = 1)

Sin = Y 0

R

Cos = X 1

R

Tan = Y 0

X

Csc = R Ø YSec = R 1

X

Cot = X Ø Y (1, 0)

y

x

5

5

-5-5

12. Find the values of the six trigonometric functions of 120°(Like #13-19)Sin = Y √ 3

R 2

Cos = X -1

R 2

Tan = Y √ 3

X -1

Csc = R 2√ 3

Y 3

Sec = R = -2

X

√3 2

-1

Cot = X √ 3

Y 3

y

x

5

5

-5-5

12. Find the values of the six trigonometric functions of 120° (Like #13-19)

√3 2

-1

y

x

5

5

-5-5

Sin

√ 3

2 Csc

2√ 3

3

Cos

-1

2 Sec

- 2

Tan

-√ 3

Cot

-√ 3

3

14. Find the values of the six trigonometric functions of 225°(Like #13-19)Sin = Y = 1

R -2

Cos = X = 1

R -2

Tan = Y 1

X

Csc = R -2

Y

Sec = R -2

X

-1

-1

Cot = X 1 2 Y

y

x

5

5

-5-5

14. Find the values of the six trigonometric functions of 225° (Like #13-19)

-1

-1 2

y

x

5

5

-5-5

Sin

2

2 Csc

2

Cos

2

2 Sec

-2

Tan 1 Cot 1

56.Evaluate 4 sec180 – 2sin2270 (Like #20-21)

4 sec180 – 2sin2270

4(-1) – 2(-1)2

- 4 – 2

- 6

57.Evaluate -cot290°+4sin270°–3tan180° (Like #20-21)

-cot290°+4sin270°–3tan180°

-(02) + 4(-1) – 3(0)

0 – 4 – 0

-4

20. Evaluate cos60 + 2sin230 (Like # 22-23)

cos60 + 2sin230

½ + 2(½)2

½ + 2(1/4)

½ + ½

1

22. Evaluate sec2300–2cos2150+tan45 (Like #22-23)

sec2300–2cos2150+tan45

22 – 2(-3/2)2 + 1

4 – 2 (3/4) + 1

4 – 1½ + 1

3½

42 The terminal side of an angle in standard position goes through the point (1,-3 ). Find the values of the six

trigonometric functions of (Like #24-25) X2 + Y2 = R2

12 + (3)2 = R2

1 + 3 = R2

4 = R2

2 = R

Sin = Y =-3

R 2

Cos = X = 1

R 2

Tan = Y =-3 X

Csc = R =-23

Y 3

Sec = R = 2

X 1

1

-3

Cot = X =-3

Y 3

y

x

5

5

-5-5

46 The terminal side of an angle in standard position goes through the point (3,-4). Find the values of the six

trigonometric functions of (Like #24-25)

Sin = Y -4R 5

Cos = X 3 R 5

Tan = Y -4 X 3

Csc = R 5

Y -4

Sec = R 5

X 3 3

Cot = X 3 -4

Y -4

y

x

5

5

-5-5

48 The terminal side of an angle in standard position goes through the point (9,-2). Find the values of the six

trigonometric functions of (Like #24-25) X2 + Y2 = R2

92 + (-2)2 = R2

81 + 4 = R2 9

85 = R2

85 = R

Sin = Y = -285 R 85

Cos = X = 985 R 85

Tan = Y = -2 X 9

Csc = R =85

Y -2

Sec = R = 85

X 9

Cot = X = 9 9

Y -2 -2

y

x

5

5

-5-5

50 The terminal side of an angle in standard position goes through the point (-22,22 ). Find the values of the six

trigonometric functions of (Like #24-25)

X2 + Y2 = R2

(-22)2 + (22)2 = R2

8 + 8 = R2

16 = R2

4 = R

Sin = Y = 2 R 2

Cos = X = -2 R 2

Tan = Y = -1 X

Csc = R = 2

Y

Sec = R = -2

X 22

Cot = X = -1 -22

Y

y

x

5

5

-5-5

66. Find the values of the six trigonometric functions of (Like #26-29)

sin = √3 , cos < 0

5

y

x

5

5

-5-5

66. Find the values of the six trigonometric functions of (Like #26-29)

sin = √3 , cos < 0 X2 +√32 = 52 5 X2 + 3 = 25 Sin = Y Csc = R X2 = 22

R Y X = 22Cos = X Sec = R √3 5

R X Tan = Y Cot = X X Y

y

x

5

5

-5-5

66. Find the values of the six trigonometric functions of (Like #26-29)

sin = √3 , cos < 0

5

Sin = Y √3

R 5

Cos = X -√22

R 5

Tan = Y -√66

X 22

Csc = R 5√3

Y 3

Sec = R - 5√22

X 22

Cot = X -√66

Y 3 5

3

y

x

5

5

-5-5

68. Find the values of the six trigonometric functions of (Like #26-29)

tan = 2, in Q3

X2 + Y2 = R2

(-1)2 + (-2)2 = R2

1 + 4 = R2

5 = R2

5 = R

y

x

5

5

-5-5

68. Find the values of the six trigonometric functions of (Like #26-29) tan = 2, in Q3

Sin = Y -25

R 5

Cos = X -√5

Tan = Y 2 -

X

Csc = R 5

Y -2

Sec = R 5

X -1

Cot = X 1

Y 2y

x

5

5

-5-5

70. Find the values of the six trigonometric functions of (Like #26-29)

sin = -2, in Q3

5

y

x

5

5

-5-5

70. Find the values of the six trigonometric functions of (Like #26-29)

sin = -2, in Q3 5 X2 + Y2 = R2

X2 + (-2)2 = 52

X2 + 4 = 25X2 = 21X = 21

y

x

5

5

-5-5

70. Find the values of the six trigonometric functions of (Like #26-29)

sin = -2, in Q3 5 Sin = Y Csc = R -5

R Y 2 Cos = X -√21 Sec = R -5√21

R 5 X 21 Tan = Y 2√21 Cot = X √21 X 21 Y 2 -2 5

y

x

5

5

-5-5

Find all values of in [0, 360) and has the given function value.

16. sin = -1/2

210, 330

18. cot = -1

135, 315

19. sec = -23/3

150, 210