Download Day 9 Review

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)
5
y
x
-5
-5
5
19  Find the angles of smallest
possible measure coterminal with
the following angles: -51 (Like #2)
5
y
x
-5
-5
5
19  Find the angles of smallest
possible measure coterminal with
the following angles: -51 (Like #2)
360°
-51°
309°
5
y
x
-5
-5
5
20  Find the angles of smallest
possible measure coterminal with the
following angles: -174 (Like #2)
5
y
x
-5
-5
5
20  Find the angles of smallest
possible measure coterminal with
the following angles: -174 (Like #2)
5
y
x
-5
-5
5
20  Find the angles of smallest
possible measure coterminal with the
following angles: -174 (Like #2)
360°
-174
186°
5
y
x
-5
-5
5
21  Find the angles of smallest
possible measure coterminal with
the following angles: 792 (Like #1)
5
y
x
-5
-5
5
21  Find the angles of smallest
possible measure coterminal with
the following angles: 792 (Like #1)
5
y
x
-5
-5
5
21  Find the angles of smallest
possible measure coterminal with
the following angles: 792 (Like #1)
792 
– 720 
72 
5
y
x
-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)
Sin =
Cos =
Csc =
Sec =
5
y
x
Tan =
Cot =
-5
-5
5
44 Find the values of the six
trigonometric functions for an
angle of 360. (Like #9-12)
Sin = Y
R
Cos = X
R
Tan = Y
X
Csc = R
Y
Sec = R
X
Cot = X
Y
5
y
x
-5
-5
5
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
Y
Sec = R 1
X
Cot = X Ø
Y
5
y
(1, 0)
x
-5
-5
5
12. Find the values of the six
trigonometric functions of 120°
(Like #13-19)
5
y
Sin
Csc
Cos
Sec
Tan
Cot
x
-5
-5
5
12. Find the values of the six
trigonometric functions of 120°
(Like #13-19)
5
√3
y
Sin
Csc
Cos
Sec
Tan
Cot
2
x
-1
-5
-5
5
12. Find the values of the six
trigonometric functions of 120°
(Like #13-19)
5
√3
Sin
y
Csc
2√ 3
3
2
x
-1
-5
-5
√3
2
Cos
-1
2
-2
Sec
5
-√ 3
Tan
Cot
-√ 3
3
14. Find the values of the six
trigonometric functions of 225°
(Like #13-19)
5
y
Sin
Csc
Cos
Sec
Tan
Cot
x
-5
-5
5
14. Find the values of the six
trigonometric functions of 225°
(Like #13-19)
y
5
-1
-1
-5
-5
Sin
Csc
Cos
Sec
Tan
Cot
x
2
5
14. Find the values of the six
trigonometric functions of 225°
(Like #13-19)
y
5
-1
-1
-5
-5
Sin
-2
2
Cos
-2
2
Sec
Tan
1
Cot
x
2
-2
Csc
-2
5
1
56.Evaluate 4 sec180 – 2sin2270
(Like #20-21)
4 sec180 – 2sin2270
5
y
x
-5
-5
5
56.Evaluate 4 sec180 – 2sin2270
(Like #20-21)
4(-1) – 2(-1)2
-4–2
-6
57.Evaluate -cot290°+4sin270°–3tan180°
(Like #20-21)
-cot290°+4sin270°–3tan180°
5
y
x
-5
-5
5
57.Evaluate -cot290°+4sin270°–3tan180°
(Like #20-21)
-(02) + 4(-1) – 3(0)
0–4–0
-4
20. Evaluate cos60 + 2sin230
(Like # 22-23)
cos60 + 2sin230
5
y
x
-5
-5
5
20. Evaluate cos60 + 2sin230
(Like # 22-23)
½ + 2(½)2
½ + 2(1/4)
½+½
1
22. Evaluate sec2300–2cos2150+tan45
(Like #22-23)
sec2300–2cos2150+tan45
5
y
x
-5
-5
5
22. Evaluate sec2300–2cos2150+tan45
(Like #22-23)
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)
Sin =
Csc =
Cos =
Sec =
Tan =
Cot =
5
y
x
-5
-5
5
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)
Sin = Y
R
Cos = X
R
Tan = Y
X
Csc = R
Y
Sec = R
X
Cot = X
Y
5
y
1
x
-3
-5
-5
5
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
5
y
1
x
-3
Csc = R =-23
Y 3
Sec = R = 2
X
Cot = X =-3
Y
3
-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 =
Csc =
Cos =
Sec =
Tan =
Cot =
5
y
x
-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
R
Cos = X
R
Tan = Y
X
Csc = R
Y
Sec = R
X
Cot = X
Y
5
y
x
-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
R
Cos = X
R
Tan = Y
X
-4
5
3
5
-4
3
Csc = R
Y
Sec = R
X
Cot = X
Y
5
-4
5
3
3
-4
5
y
3
x
-4
-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)
Sin =
Csc =
Cos =
Sec =
Tan =
Cot =
5
y
x
-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)
Sin = Y
R
Cos = X
R
Tan = Y
X
Csc = R
Y
Sec = R
X
Cot = X
Y
5
y
9
x
-2
-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
85 = R2
85 = R
Sin = Y = -285 Csc = R =85
R
85
Y -2
Cos = X = 985 Sec = R = 85
R 85
X
9
Tan = Y = -2
Cot = X = 9
X 9
Y -2
5
y
9
x
-2
-5
-5
5
50 The terminal side of an angle  in
standard position goes through the point
(-22, 22). Find the values of the six
trigonometric functions of (Like #24-25)
Sin =
Csc =
Cos =
Sec =
Tan =
Cot =
5
y
x
-5
-5
5
50 The terminal side of an angle  in
standard position goes through the point
(-22, 22). Find the values of the six
trigonometric functions of (Like #24-25)
Sin = Y
R
Cos = X
R
Tan = Y
X
Csc = R
Y
Sec = R
X
Cot = X
Y
5
y
22
-22
-5
-5
x
5
50  The terminal side of an angle  in
standard position goes through the point
(-22,22 ). Find the values of the six
trigonometric functions of (Like #24-25)
X2 + Y2 = R2
(-22)2 + (22)2 = R2
8 + 8 = R2
16 = R2
4=R
Sin = Y = 2
Csc = R = 2
R 2
Y
Cos = X = -2 Sec = R = -2
R
2
X
Tan = Y = - 1 Cot = X =-1
X
Y
y
5
22
x
-22
-5
-5
5
66. Find the values of the six
trigonometric functions of 
(Like #26-29)
sin  = √3 , cos  < 0
5
5
y
x
-5
-5
5
66. Find the values of the six
trigonometric functions of 
(Like #26-29)
sin  = √3 , cos  < 0
5
Sin = Y
Csc = R
R
Y
Cos = X
Sec = R
R
X
Tan = Y
Cot = X
X
Y
X2 +√32 = 52
X2 + 3 = 25
X2 = 22
X = 22
√3
5
5
y
x
-5
-5
5
66. Find the values of the six
trigonometric functions of 
(Like #26-29)
sin  = √3 , cos  < 0
5
Sin = Y √3 Csc = R 5√3
R5
Y 3
Cos = X -√22 Sec = R -5√22
R 5
X 22
Tan = Y -√66 Cot = X -√66
X 22
Y 3
5
√3
y
5
x
-5
-5
5
68. Find the values of the six
trigonometric functions of 
(Like #26-29)
tan  = 2,  in Q3
5
y
x
-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
5
y
x
-5
-5
5
68. Find the values of the six
trigonometric functions of 
(Like #26-29)
tan  = 2,  in Q3
Sin = Y -25
Csc = R 5
R 5
Y -2
Cos = X -√5
Sec = R 5
R 5
X -1
Tan = Y 2
Cot = X 1
X
Y 2
y
5
-1
x
-2
-5
-5
5
70. Find the values of the six
trigonometric functions of 
(Like #26-29)
sin  = -2,  in Q3
5
5
y
x
-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 = 25
X2 = 21
X = 21
5
y
x
-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
Cos = X -√21 Sec =
R 5
Tan = Y 2√21 Cot =
X 21
R -5
Y 2
R -5√21
X 21
X √21
Y 2
y
5
x
-2
-5
-5
5
5
Find all values of  in [0, 360)
and has the given function value.
(Like #30-33)
16. sin  = -1/2
18. cot  = -1
19. sec  = -23/3
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  = -23/3
150, 210