Review for Test 3 MAT 146
1.) Find the missing quantity to tow decimal places given s is the arc length corresponding to a
central angle θ on a circle of radius r.
a) r = 7inches,  
3
;s=?
14
b) s = 6ft,  

7
;r=?
2.) A point on the rim of a circular water wheel of radius 8ft makes one complete rotation every
10 seconds. Find the angular and linear speeds of the circular motion of the moving point.
3.) A bicycle’s small sprocket wheel of radius 2.75 inches is connected by a chain to a large
sprocket wheel of diameter 9 inches. The small sprocket wheel turns at 50 rotations per minute.
Find the linear speed (in inches per minute) of the chain connecting the sprocket wheels.
4) A trail bike has a front wheel with a diameter of 30 centimeters and a back wheel of diameter
90 centimeters. Through what angle in radians does the front wheel turn if the back wheel turns
through 10 radians?
5) Find the coordinates of each circular point :
  9 
 11 
a) W 
b) W 


 4 
 3 
 7 
c) W 

 2 
  5 
d) W 

 6 
6) Using your answers to problem 5 given the exact value of the following:
  9 
a) sin 

 4 
 11 
b) tan 

 3 
  5 
e) cot 

 6 
 11 
f) cos

 3 
  5 
c) sec

 6 
 7 
d) csc

 2 
  4 3
, .
7) Find the exact value of the six trigonometric functions given W 
 5 5
a) sin x =
b) cos x = c) tan x = d) csc x = e) sec x = f) cot x =
8) Find the exact value of the expression given that x is an angle in standard position and the
terminal side of x contains the indicated point.
a) cos x ; (−1, −3) b) sin x; (2, −1) c) sec x; (−9. −40) d) cot x; (−8, 15)
9) Use the figure and given information to solve the following triangle:
10) Find the value of each of the other five trigonometric functions for an angle θ, without
finding θ, given the information indicated.
7
cot t < 0
25
b) sec θ =
5
sin θ < 0
3
c) tan t = −3 cos t > 0
d) cot θ =
3
sin θ < 0
4
a) sin t =
11) Without finding θ, find the values of each of the six trigonometric functions for an angle θ
whose terminal side contains the point.
a) (1, 3) b) (−4, −1)
12) Is y 
sec x
an odd or even function?
x
13) Is y = x3 sin x an odd or even function?
14) Find the amplitude and period for the following :
a) y 
1
1
cos 2 x b) y  3 sin x
5
2
e) y 
1
tan 3x
4
2
x
c) y   cos
3
3
d) y  3 sin
f) y  3 csc x
15) Find the amplitude, period and phase shift for the following:


a) y  3 sin  x  
3



b) y  2 cos x   c) y  3 sin 4 x  1
3

d) y  4 cos(1  3x)


e) y  4 csc x   f) y = 2tan 3x
2

x
2