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Name ________________________
Math Analysis
Test #05: Trigonometric Functions of Angles
Assigned: Tuesday 11/22/2005
Due: Monday 11/28/2005
Score: __ / 167
 2
1. It is a fact that cos 
 5
5 1

.

4

2
a. ( __ / 2 ) Convert
into degrees.
5
 2
b. ( __ / 5 ) Give an exact expression for: sin 
 5



 2
c. ( __ / 2 ) Give an exact expression for: tan 
 5



 2
d. ( __ / 2 ) Give an exact expression for: cot 
 5



 2
e. ( __ / 2 ) Give an exact expression for: sec 
 5



 2
f. ( __ / 2 ) Give an exact expression for: csc 
 5



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2. ( __ / 15 ) Solve the triangle below.
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3. ( __ / 30 ) Solve the two triangles below.
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4. ( __ / 15 ) Solve the triangle below.
5. ( __ / 15 ) Solve the triangle below.
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6. ( __ / 15 ) Two vertical poles, one 32 feet tall, and the other 20 feet tall, are placed 15 feet apart. Guy
wires connect the top of each pole with the bottom of the other. Find the angle  formed by the
intersecting guy wires.
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7. A certain garden design calls for an arc-shaped patio made from brick, as shown in the picture
below. The outside radius of the patio is 22.4 feet, while the inside radius is 11.0 feet. The angle of
the arc is 53°.
a. ( __ / 10 ) What is the area of the shaded region?
b. ( __ / 10 ) What is the perimeter of the shaded region?
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8. ( __ / 10 ) Find the area of the shaded region below.
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5 1
 2 
9. The purpose of this problem is to derive the fact that cos 
. To begin, consider an

4
 5 
isosceles triangle whose congruent sides are of length 1 and whose base is of length x, as shown in
the image below. The angles are chosen so that the vertex angle is half of either of the base angles.
a. ( __ / 5 ) How big are the vertex and base angles?
b. ( __ / 5 ) Bisect one of the base angles, then show that the triangle formed is similar to the
original triangle. (Recall: similar triangles have equal angles, and their sides are proportional in
length.) Use this fact to calculate x.
 2
c. ( __ / 5 ) Now calculate cos 
 5
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
.

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10. ( __ / 10 ) Calculate the area of the quadrilateral below, correct to 2 decimal places.
11. The sprockets and chain of a bicycle are shown in the picture below. The pedal sprocket has a radius
of 4 inches, while the wheel sprocket has a radius of 2 inches, and the wheel has a radius of 13
inches. The cyclist pedals at 60 RPM.
a. ( __ / 5 ) Find the angular speed of the wheel sprocket.
b. ( __ / 5 ) Find the speed of the bicycle.
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