Trigonometry
Final Review
Name ____________________________________
1.) Convert the angle in degrees to radians. Express the answer as a multiple of π. 180
2.) Convert the angle in degrees to radians. Express the answer as a multiple of π. 270
3.) Convert the angle in radians to degrees.
3
4
4.) Convert the angle in radians to degrees. 

4
6.) Find the exact value. cot 90

2
5.) Find the exact value. sin
7.) If cos  
2
, find sec .
3
8.) Name the quadrant in which the angle  lies.
cos   0, csc   0
9.) If sin  
1
10
and cos   , find tan  .
3
3
10.) Match the given function to its graph.
1. y  sin x
A.
B.
2. y  cos x
3. y   sin x
C.
4. y   cos x
a.) 1A, 2B, 3C, 4D
b.) 1C, 2A, 3B, 4D
c.) 1B, 2D, 3C, 4A,
d.) 1C, 2D, 3B, 4A
11.) What is the y-intercept of y  cos x ?
D.
Trigonometry
Final Review
1 
x .
2 
12.) State the amplitude for y  5sin 
13.) State the period for y  3cos  2 x  .
14.) Write the equation of the sine function that has the given characteristics.
Amplitude: 4
Period: 3π
15.) Write the equation of the sine function that has the given characteristics.
Amplitude: -2
Period: π
Phase Shift: 3
 1
 2

3
1
17.) Find the exact value. cos  
 2 


16.) Find the exact value. sin 1   

18.) Find the exact value. tan 1  3

19.) Use the sum and difference identities to find the exact value. sin165
20.) Use the sum and difference identities to find the exact value. tan15
4
5
For 21 & 22, use the information given about the angle α to find the exact value of each. sin    ,
 

2
21.) cos  2 
3
   2
2
22.) sin 
For 23-25, solve each equation on the interval 0    2 .
23.) tan   1
24.) cos  2  
2
2
25.) sin 2   sin   1  cos 2 
For 26-28, use the figure.
26.) Find cos .
27.) Find csc .
28.) Find tan  .
29.) A 15-foot ladder just reaches the top of a house and forms an angle of 52° with ground. How tall is the house?
Trigonometry
Final Review
30.) Given A  15, B  80, b  4 , find a.
31.) Given A  15, B  80, b  4 , find c.
32.) Given a  12, b  5, c  8 , find A.
5 

4 
34.) Find the polar coordinates of the point given in rectangular coordinates.  2, 2 


33.) Find the rectangular coordinates of the point given in polar coordinates.  2,
35.) The letters x and y represent rectangular coordinates. Write the equation using polar coordinates  r ,   .
x2  y 2  9 y
36.) The letters r and  represent polar coordinates. Write the equation using rectangular coordinates  x, y 
r  8cos
37.) Write the complex number in polar form. Express the argument in degrees. 1  3i
38.) Write the complex number in rectangular form.
39.) Find zw. Leave your answer in polar form.
40.) Find
5
5 

4  cos
 i sin

6
6 

z  2  cos130  i sin130 
w  4  cos 40  i sin 40 
z  2  cos130  i sin130 
z
. Leave your answer in polar form.
w
w  4  cos 40  i sin 40 
3
 

 
41.) Write the expression in standard form a  bi .  2  cos  i sin  
4
4 
 
42.) The vector v has initial point P and terminal point Q. Write v in the form ai  bj ; that is, find its position vector.
P   1,3 ; Q   2, 5
43.) Given v  3i  5 j and w  7i  4 j , find 2v  4w .
44.) Given v  3i  5 j and w  7i  4 j , find v  w .
45.) Find the unit vector having the same direction as v  2i  3 j .
46.) Find a rectangular equation for the plane curve defined by the parametric equations. x  t 2 , y  t  3,  2  t  2
47.) A baseball pitcher throws a baseball with an initial speed of 150 feet per second at an angle of 22° to the horizontal.
The ball leaves the pitcher’s hand at a height of 5.5 feet. Find parametric equations that describe the motion of the
ball as a function of time.