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Final Exam Review – cumulative section of the final exam
Math 124
1. Find the 5 remaining trigonometric function values for the angle  csc  3 ,  is in QIV
2. Consider the point  5, 6 
a. Sketch the angle  in standard position such that  has the least possible positive measure,
and the given point is on the terminal side of 
b. Find the value of the six trigonometric functions for the angle in part (a)
3. An equation of the terminal side of an angle  in standard position is given with a restriction on x.
4x  7 y  0 , x  0
a. Sketch the least positive such angle 
b. Find the values of the six trigonometric functions for the angle in part (a).
4. Evaluate without a calculator
a. sin 2 180  sin 360  cos180
b. sin120
c. cot 330
d. sin1500
e. tan 3015
 5 
sin  
 6 
 2 
g. cot  

 3 
f.
5. Evaluate. Give as many digits as your calculator displays.
a. sin123 4216
b. sec  65 45 
6.
a. Find a value of  in the interval 0 ,90  such that sec  2.1352158 . Give as
many digits as your calculator displays.
b. Find all values of  in the interval 0 ,360
 such that cos  
c. Find the exact value of s in the given interval.
cos s 
1
,
2
3
2
 3

 2 , 2 
7. Solve the right triangle given A  13 47 , c  1285 cm
8. A 13.5-m fire truck ladder is leaning against a wall. Find the distance d the ladder goes
up the wall (above the top of the fire truck) if the ladder makes an angle of 43 50 with
the horizontal. (Problem number 41 in section 2.4 – see text for figure.)
9. Two ships leave a port at the same time. The first ship sails on a bearing of 40 at 18
knots (nautical miles per hour) and the second at a bearing of 130 at 26 knots. How far
apart are they after 1.5 hours?
1
10. Graph each function over a one-period interval. State the period, amplitude, phase shift,
vertical shift, and vertical asymptotes, if applicable.
c. y  4sec  2 x 
1

a. y  3sin  x     1
2



b. y  cot  3x  
4

11. Verify the identity
a. sin 2   tan 2   cos2   sec2 
tan x
sin x
b.

 cot x  sec x csc x
1  cos x 1  cos x
c. 1  cos 2 x  cos2 x  cos2 x
d.
sin  x  y 
sin y

cos  x  y 
cos y

sin x
sin y cos y
2
5
, sin t  
, s and t in QIV
4
6
5
13. Find the values of sin  2x  and cos  2x  given tan x  and sin x  0
3
3
3
x
x
 x
14. Find the values of sin   , cos   and tan   given cos x   and   x 
7
2
2
2
2
12. Find cos  s  t  and sin  s  t  given that cos s 
15. Give the degree measure of 
 1
a.   arccos   
 2

2
b.   arcsin  
 2 


c.   arcsin  2 

d.   tan 1  3

e.   arc cot  3

 3
f.   arcsin 

 2 
g.   arc csc  2 

16. Give the exact value of each expression
2

a. cos  sin 1 
3

c. sin  2sin 1 1

 7 
b. tan  cos 1    
 12  

2