Download 13.3 Worksheet

Algebra 2
13.1 – 13.3 Worksheet (Radians)
Show all work for full credit.
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1) Draw an angle with the given measure in standard position.
a)
5
4
b) 

c)
3
7
3
2) Find one positive angle and one negative angle that are coterminal with the given angle.
a) 
2
3
Positive angle:
Negative angle:
b)
5
4
Positive angle:
3) a) Find the arc length and b) area of a sector with radius 4 cm. and central angle  
and then to the nearest hundredth.
Arc length:
11
6

3
. Give exact answer,
Area of sector:
4) Evaluate the six trigonometric functions of . (No calculator.)
a)  =
Negative angle:
sin  
csc  
cos  
tan  
b)  =
2
3
sin  
csc  
sec  
cos  
sec  
cot  
tan  
cot  
5) Evaluate the function without using a calculator.
a) sin
4
3
b) tan
3
4
c) sin
e) cot
11
6
f) tan

6
g) cot
i) cos
 5
6
j) csc
5
3
k)
 3
2
 2
3
cos 3
d) cos
 7
6
h) cos
5
6
k)
5
2
tan
6) Additional Story Problem Practice: (Draw and label a picture if none is given. Round to the nearest hundredth and include units.)
a) A pizza is cut into six pieces. Each piece represents an equivalent sector of the pizza. Find the measure of the
angle formed by four pieces of pizza. Give the answer in radians.
b) The pendulum of a grandfather clock is 3 feet long and swings back and forth creating a
the arc created by the pendulum after one swing.

4
angle. Find the length of

4
c) A hill that is used for sledding has an angle of elevation of 32°. If the length of the ride down the hill is 52.6 feet,
estimate the height of the hill.
d) From the top of Goat Island Lighthouse, the angle of depression to a ship at sea is 2°. If the lighthouse is 60 feet
above sea level, find the distance from the base of the lighthouse to the ship.
e) A telegraph pole is stayed by wires to the ground from a point 20 feet up the pole. Each of the wires makes an angle
of 24° with the vertical pole. Find the length of the wire.
f) A balloonist records her altitude as 1208 meters. At the same time, she measures the angle of depression of the landing spot to
be 17 degrees. How far away is the landing spot from a point on the ground vertically below the balloonist?