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Math 1113 Practice Test 2 Fall 2013
0. (2points if it is printed neatly) Name:______________________________
To get any credit you must show all applicable work. You will not get credit for a question in which you
draw a triangle with a negative side. That is, angles must be sketched correctly in standard position.
1. Sketch 210° in standard position
2. Find two angles, one positive and one negative, that are coterminal with 135°
3. Convert 
3
to degrees without using a calculator
5
4. Find the exact values of the six trigonometric functions of 
13

12
5. Find the exact value of  in radians, 0   
special triangles we use for special angles.

2
, without using a calculator. First draw the two
(a) cos  
2
2
(b) sin  
3
2
(c) tan  
3
3
6. Find the exact values of the six trigonometric functions of  if (2, −3) is a point on the terminal side of
 in standard position.
7. Without using a calculator evaluate: (Draw the angle in standard position and use a definition, for
example, sin  
(a) cos 
y
)
r
(c) sec2
(b) tan 270
8. Find the reference angle for each of the following angles:
(a)   25
(b)  
7
6
(c)   480
9. Put the correct sign in the box. That is, put + or – in the box.
(a) tan  
tan  ',
 is in QIII
(b) sin  
sin  ',
 is in QIV
(c) cos 
cos ',
 is in QIV
1
2
10. Without using a calculator find two solutions of the equation cos   . Give your answers in
degrees with 0    360
11. A tree casts a shadow 20 feet long when the angle of elevation of the sun is 58°. How tall is the
tree?
12. Maggie is flying her kite using 50 feet of string, holding the string next to the ground. Sabra is 30
feet way from Maggie and notices that the kite is directly over her head. How high is the kite?
13. Without using a calculator graph one cycle of y  2 cos(3x   ) . To get credit you must make it
clear how you determine the endpoints of the cycle you graph.
14. Without using a calculator graph one cycle of y  3sin(2 x   ) . To get credit you must make it
clear how you determine the endpoints of the cycle you graph.
15. Without using a calculator graph one cycle of y  3cot(2 x 

2
) . To get credit you must make it
clear how you determine the endpoints of the cycle you graph.
16. Find the length of the third side of the triangle in terms of x. Then find  in terms of x for all three
inverse trigonometric functions.
5

x
17. Without using a calculator find the exact value of sin 1 (sin
7
).
4
18. Without using a calculator find the exact value of tan(arcsin( 34 ))
B
c
a
C
b
A
19. Solve the triangle if A  28 and a  12.3 . Round answers to three decimal places.
20. Finding the height of a Flagpole. A flagpole is mounted on the edge of a tall building. From a point
30 feet from the bottom of the building the angle of elevation of the bottom of the flagpole is 60, and
the angle of elevation of the top of the flagpole is 70. How tall is the flagpole?