Short Answer Review Answers Name KEY

Short Answer Review Answers
1. Express 240° in radian measure.
240π
4π
=
180 3
2. In a circle, a central angle of 3 radians
intercepts an arc of 15 centimeters. Find the
length of the radius in centimeters.
s = θr
15 = 3r
5 = r
3
3. If x is a positive acute angle and cos x = ,
5
find the value of sin x .
Name KEY
8. Find the value of sin 37° 34' to four decimal
places.
sin 37° 34' = 0.6097
⎛ 1 ⎞
9. If y = tan ⎜Arccos ⎟, then y equals:
⎝ 2 ⎠
(1) 45° (2) 60°
1
(3) 3 (4)
3
tan ( 60° ) = 3
Quadrant I
4
sin x =
5
10. What is cos 68° 20'
(1) 0.9315 (2) 0.9293
(3) 0.3638 (4) 0.3692
⎛ 3 ⎞
4. Find the value of cos⎜Arcsin ⎟
⎝ 5 ⎠
4
5
⎛ 3 ⎞
11. What is the value of cos ⎜
Arcsin 2 ⎟
⎝ ⎠
1
cos( 60° ) =
2
5. Express 160° in radian measure.
160π
8π
=
180 9
4
6. If sinθ =− and tanθ is negative, what is
5
the value of cosθ
12. Express tan ( − 140)
as a function of a
positive acute angle.
tan ( − 140° ) = tan 220°= tan 40°
13. Find the value of Arc tan 3 .
Arc tan 3 = 60°
In QIV, sin and
tan are negative.
3
cosθ =
5
7. Express 5 π radians in degree measure.
9
5π
5•
180
= = 100 °
9 9
14. Find the value of acute A if
sin A = cos50
A + 50 = 90
A = 40°
sin A = 1.
cos50°

15. In a circle with a radius of 2.5 centimeters, a
central angle has a measure of 5 radians.
What is the length, in centimeters, of the arc
intercepted by the central angle
s = θ r
s = (5)(2.5)
s = 12.5cm
16. If tan x =− 3 and sin x > 0, then angle x
terminates in Quadrant:
(1) I (2) II (3) III (4) IV
In QII, sin is positive and tan is negative.
⎛π
⎞
22. If f ( x) = cos2x, find f ⎜ ⎟
⎝ 2 ⎠ .
⎛π
⎞ ⎛π
⎞
f ⎜ ⎟= cos 2⎜ ⎟= cosπ
=−1
⎝ 2⎠ ⎝ 2⎠
23. What is the smallest positive value of x that
1
satisfies x= Arccos 2
1
Arc cos = 60°
2
17. Find the value of tan120° .
tan120°=−
3
18. What is the numerical value of the product
cosπ sinπ
of ( )( )
( cosπ)( sin π ) = ( − 1)(0) = 0
19. Which expression is equivalent to
sin − 120°
( )
(1) sin 60° (2) − sin 60°
(3) sin 30° (4) − sin 30°
sin ( − 120° ) = sin 240°=− sin 60°
20. If cos3x°=
sin 60°, then x may equal:
(1) 10 (2) 20 (3) 30 (4) 40
3x
+ 60=
90
3x
= 30
x = 10
21. If placed in standard position, an angle of
11
π radians has the same terminal side as
6
an angle of:
(1) − 150° (2) − 30°
(3) 150° (4) 240°
11 11•
180
π = = 330°=− 30°
6 6
24. Which is equal in value to sin180°
(1) tan 45° (2) cos90°
(3) cos 0° (4) tan 90°
sin180°=
0
cos90°=
0
25. Express 210° in radian measure.
210π
7π
=
180 6
26. cos 280° is equivalent to:
(1) − sin 80° (2) − cos80°
(3) cos10° (4) cos80°
cos 280°= cos80°
27. If sinθ = 0.5035 , find the value of positive,
acute angle θ to the nearest minute.
30° 13'54.586" ≈ 30°
14'
2
28. If sin x = − and sin xcos x> 0 , in which
3
quadrant does angle x lie
(1) I (2) II (3) III (4) IV
sin x is negative and since sin x cos x is
positive, cos x also must be negative.
In QIII, both sin and cos are negative.