Download Algebra 2/Trigonometry Honors Name: Homework (14.2-14.3)

Algebra 2/Trigonometry Honors
Name:
Homework (14.2-14.3)
Set A --- Coordinate Definitions and the Unit Circle
1. Refer to the figure.
a. Find the value of y.
b. Find cos .
c. Find sin .
2. Given that 0    360 , find  for each of the following.
a.
sin   1
b.
sin   1
c.
sin2   1
d.
cos2   1
3. Find the exact value of each of the following.
a.
cos210
b.
sin240
c.
tan150
d.
sec300
e.
cot180
f.
sin( 30 )
In problems 4-6, let (x, y) be a point on the terminal ray of , and let (x, y) be r units from the origin.
4. Find sin  if x = 5 and r = 13.
5. Find cos  if x = 8 and y = 15.
6. Find tan  if x = 8 and r = 10.
7. Let (-7, 24) be a point on the terminal ray of an angle  in standard position. Find the six trig functions of .
8. Solve for y, where
a.
0  y  360 .
tan2 y  1
9. Find all values of  for which
a.
cos  
b.
sec2 y  1
c.
360    360 and
 2
2
b.
tan   1
10. Find the exact coordinates of point Q.
11. If 0    360 , what values of  satisfy each equation?
a. cos  
c.
1
2
cos2   1  0
b. cos
2
d.

1
2
cos2   cos   0
sin y  cos y
14.2-3 SET A - ANSWERS
1. a) 2 21 b)
2
c)
5
21
5
2. a) 90 b) 270 c) 90 or 270 d) 0, 180, or 360
3. a)

4. 
12
13
5.
3
3
3
1
b) 
c) 
d) 2 e) Undefined f) 
2
2
3
2
8
17
6. 
3
4
7. sin  
24
7
24
;cos   
;tan   
25
25
7
8. a) 45, 135, 225, or 315 b) 0, 180, or 360 c) 45 or 225
9. a) -225, -135, 135, 225 b) -225, -45, 135, 315
10.
( 4, 4 3)
11. a) 60 or 300 b) 45, 135, 225, or 315 c) 0, 180, or 360 d) 0, 90, 270, or 360
Algebra 2/Trigonometry Honors
Name:
Homework (14.2-14.3)
Set B --- Using the Calculator and Pythagorean Identities
1. Find each first-quadrant angle described.
a.
sin   0.3874
d. tan  
4
3
b. cos  
8
17
e. cos  
1
10
c. sin  
f.
1
7
sin   1.342
2. Given that  = 72, calculate each value to the nearest thousandth.
a. sin 
b. cos (90 - )
c. tan 
d. cot (90 - )
3. The area of triangle OAC is 5. Find each of the following.
a. The coordinates of point C
b. OC
c. The coordinates of point B.
d. mAOC
4. Find each value to the nearest thousandth.
a. The coordinates of point A
b. The area of triangle AOB
5. For each point on the unit circle, find the measure of the angle whose terminal ray passes through the point.
a. (0, -1)
c.
4 3
 , 
5 5
b.

2
2
,


 2
2 

d. (0.819, 0.573)
6. If cos  = 0.695, what is the value of each of the following?
a. sin 
b. tan 
c. sec 
7. Let sec  = 4.25. Find all possible values of  such that 0    360.
8. Simplify each expression in terms of a single trig function.
a.
(1  sin  )(1  sin  )
sin2 
 cos2 
b. sin  
2
cos 
2
9. Refer to the figure.
a. Find cos , sin , and tan .
b. Find the value of .
10. Find an expression in terms of a and b for each of the following.
a. tan 
b. sin (180 - )
c. cos (360 - )
d. tan ( + 180)
e. cos (180 + )
f. sin (360 - )
11. Find the exact values of sec  for which tan  
12
.
13
c.

1 
(sec  )  cos  

cos  

14.2-3 SET B - ANSWERS
1. a) 22.79, b) 61.93, c) 8.21, d) 53.13, e) 84.26, f) Impossible
2. a)  0.951 b)  0.951 c)  3.078 d)  3.078
3. a) (1, 10), b)
101 , c) (
101 10 101
,
) , d)  84.29
101
101
4. a) ( 0.342,  0.940) b)  0.470
5. a) 270, b) 225, c) 323.13, d) 35
6. a)   0.719, b)   1.035, c)  1.439
7.  76.39 or  283.61
8. a)
cos2  , b) sec2  , c)  tan2 
9. a)

6 85 7 85 7
;
;  , b)  130.60
85
85
6
10. a) b/a, b) b, c) a, d) b/a, e) –a, f) –b
11.
313
313
or 
13
13