Name__________________________
Trig Review 13.1-13.3
Evaluate the six trigonometric functions of the angle Θ.
1.
sin Θ =_____ sec Θ = _____
2.
sin Θ =_____ csc Θ = _____
cos Θ = _____ csc Θ = _____
cos Θ = _____ sec Θ = _____
tan Θ = _____ cot Θ = _____
tan Θ = _____ cot Θ = _____
2.
If Θ is an acute angle of a right triangle and cos  
3
, what is the value of the csc .
8
3.
If Θ is an acute angle of a right triangle and sec  
12
what is the value of the tan 
5
Find the value of each variable. Write your answer in simplest radical form.
4.
5.
6.
You are hiking toward a main road, but reach a point where the road is flooded. To avoid the flooded area, you
turn onto a diagonal road that meets your original road at a 48⁰ angle and follow that road for 3.6 miles until
you hit the main road. How far were you from the main road when you turned onto the diagonal road?
5.
From a point on the ground 28 feet from the base of a flagpole, the angle of elevation to the top of the flagpole
is 63⁰. Estimate the height of the flagpole.
Draw an angle with the given measure in standard position.
6.
150
7.
8
5
8.

11
3
9.
700
13.
11
6
Find one positive angle and one negative angle that are co terminal with the given angle.
10.
-215⁰
11.
570⁰
12.

2
3
Convert the given angle measure.
14.
75 to radians
15.

15
radians to degrees
7
16.
Children at a day camp are playing a game on a circular field. The shaded sector in the
figure is called the “safe zone”, and is marked off by rope along its outer edge. Find the
length of the rope and the area of the safe zone.
120˚
18ft
Use the given point on the terminal side of an angle  in standard position to evaluate the six trigonometric functions.
( 9, 40)
17.
sin Θ =_____ sec Θ = _____
18.
(7, 2)
sin Θ =_____ csc Θ = _____
cos Θ = _____ csc Θ = _____
cos Θ = _____ sec Θ = _____
tan Θ = _____ cot Θ = _____
tan Θ = _____ cot Θ = _____
Use the unit circle to evaluate the six trigonometric functions of  .
  0
17.
sin Θ =_____ sec Θ = _____
18.
 
5
2
sin Θ =_____ csc Θ = _____
cos Θ = _____ csc Θ = _____
cos Θ = _____ sec Θ = _____
tan Θ = _____ cot Θ = _____
tan Θ = _____ cot Θ = _____
Sketch the angle. Then find its reference angle.
7
12
19.
20.
295
21.

8
3
22.
370
Evaluate without using a calculator.
23.
27.
sin(225)
24.
cot
5
3
25.
cos
11
6
26.
tan330
Your school’s marching band is performing at halftime during a football game. In the last formation, the band
members form a circle 100 feet wide in the center of the field. You start at a point on the circle 100 feet from
the goal line, march 330 around the circle, and then walk toward the goal line.
a.
How far from the goal line are you at the point where you leave the circle?
b.
How far do you march around the circle?