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Mathematics 120 test four
Monday, December 6, 2004
please show your work to get full credit for each problem
no calculators on this test
2π
radians to degrees.
3
1. Find the reference angle of 215◦ .
2. Convert
3. Find two other angles which share a
terminal side with the angle −45◦ .
4. A central angle θ in a unit circle
intercepts an arc of length 2. Find the
radian measure of the angle θ.
s=2
θ
r=1
5. An central angle of 20◦ sits in a circle of radius 4000.
What is the length of the intercepted arc?
20°
r=400
s=?
6. The equation sin−1 n = θ is equivalent to the statement
where
≤θ≤
page two
7. Evaluate each of the following quantities:
(a) sin
(e) sin
π
3
−1
(b) cos
1
2
3π
4
−1
(f) cos
(c) tan (−30◦ )
√ !
3
−
2
2
(g) tan arccos
3
(d) sec
8. Sketch a graph of
1
π
x−
.
30
3
The sketch should include the exact location of all quarter-cycle points.
y = 20 cos
2π
3
page three
y
50
x
-.01
.02
.05
.08
.11
-50
9. Given the graph of a modified sine graph above, find each of the following:
(a) amplitude =
(b) period =
(c) frequency =
(d) shift =
(e) equation of this graph:
10. Find two angles between 0 and 360◦ which solve each of the following equations:
(refer to the unit circle diagram)
(a) cos θ = 0.2
(b) sin θ = −0.4
(c) tan θ = −1
page four
11. Solve each of the following triangles for the indicated quantities:
(a)
400
y
1
(b)
θ
60°
3
x
(c)
L
45°
8
30°
x