Exam
Name___________________________________
A) Quadrant III
B) Quadrant II
C) Quadrant I
D) Quadrant IV
1)
Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure
of two other angles, one positive and one negative, coterminal with the given angle.
2)
410° and -310°
A) 230° and -130°
B)
C)
D)
410° and -310°
230° and -130°
3)
C.
m A = 63°
m E = 35°
A) 35°
B) 63°
C) 92°
D) 82°
4)
a = (x + 19)°
b = (x + 81)°
A) 70°, 70°, 40°
B) 40°, 39°, 101°
C) 20°, 40°, 120°
A)
C)
B)
D)
1
D) 20°, 40°, 30°
5)
A) 127°
A) 310.33°
B) 143°
C) 53°
B) 310.34°
C) 310.39°
D) 217°
D) 310.29°
6)
7)
Place your graphing calculator in parametric and degree modes. Set the window for Tmin=0, Tmax=360, Tstep=1, Xmin=
-1.8, Xmax=1.8, Xscl=1, Ymin= -1.2, Ymax=1.2, Yscl=1. Set the functions to X1T=cos T, Y1T=sin T. Graph the circle of
radius 1 on the screen. Use the trace feature to move a short distance around the circle.
A) 60°
B) 28.65°
C) 0.866°
D) 30°
9)
Find the measure of the smaller angle formed by the hands of the clock shown.
A) 110°
B) 60°
C) 120°
D) 150°
10)
AC
A)
C)
B)
D)
A) csc 48.5°
B) cos 48.5°
C) csc 41.5°
D) cos 138.5°
3 2
s
6
B)
3 2
s
2
C)
2
11)
12)
Find a formula for the area of the figure in terms of s.
A)
8)
6 s2
D)
6 2
s
4
Find the equation of a line passing through the origin so that the cosine of the angle between the
1
line in quadrant I and the positive x-axis is .
2
A) y =
1
x
2
B) y =
C) y =
3x
3
x
2
D) y =
13)
3
x
3
14)
A) 2
2 3
B)
3
2 3
C) 3
D) 2
A) 112.7°
B) 22.7°
C) 157.3°
D) 67.3°
sin
=-
1
2
A) 60° and 300°
15)
16)
B) 150° and 210°
C) 210° and 330°
D) 60° and 120°
The figure shows an angle in standard position with its terminal side intersecting the unit circle. Evaluate the indicated
circular function value of .
Find cot .
17)
7
24
,25
25
A) -
7
24
B) -
24
7
C)
3
7
24
D)
24
7
A) Multiply the degree measure by
C) Multiply the degree measure by
tan
360°
180°
.
B) Multiply the degree measure by
.
D) Multiply the degree measure by
180°
90°
18)
.
.
5
4
A)
19)
3
3
A) 2
B) 1
C)
3
B)
2
5
C)
2
3
D) 1
20)
D) 4
An equation of the terminal side of an angle in standard position is given along with a restriction on x. Find the
indicated trigonometric function value of . Do not use a calculator.
21)
5 61
61
6
5
A) B) C) D) 5
6
61
5
Find csc , given that sin
A) -
3
2
A) 0
=-
B)
2
and
3
22)
is in quadrant IV.
5
4
C) -
B) 5
7
9
C) Undefined
D)
3 7
7
23)
D) 5
A person is watching a car from the top of a building. The car is traveling on a straight road directly
toward the building. When first noticed, the angle of depression to the car is 27° 4 . When the car
stops, the angle of depression is 49° 11 . The building is 210 feet tall. How far did the car travel from
when it was first noticed until it stopped? Round to the nearest foot.
A) 430 ft
B) 230 ft
C) 209 ft
D) 256 ft
24)
25)
A)
3
3
B) -
3
3
C)
4
3
D) -
3
A) II
B) I
C) III
D) IV
An alien observer on Planet X can approximate distances in the sky by using his "hand" at arm's
length. An outstretched hand is about 30 arc degrees, a clenched fist is about 20 arc degrees, and a
thumb corresponds to about 1 arc degree. (i) If one clenched fist plus one outstretched hand covers
the distance between two stars, about how far apart in arc degrees are the stars? (ii) The apparent
size of Moon X as observed from Planet X is about 21 arc minutes. Approximately what part of an
observer's thumb would cover Moon X?
1
A) (i) 51 arc degrees; (ii) approximately of a thumb
5
B) (i) 21 arc degrees; (ii) approximately
1
of a thumb
2
C) (i) 40 arc degrees; (ii) approximately
1
of a thumb
4
D) (i) 50 arc degrees; (ii) approximately
1
of a thumb
3
27)
28)
a = 2.4 in., A = 51.6°, C = 90°
Round values to one decimal place.
A)
C)
9
A)
2
26)
B)
D)
9
B) 2
9
C) 4
29)
D) 9
30)
A) 1
B) Undefined
C)
5
2
2
D) 0