Download Math110 Final Exam S

Final Exam
Math110
Sample
1. A radial saw has a blade with a 12 inches radius. Suppose that the blade spins
at 1400 revolution per minute.
a. Find the angular speed of the blade in rad/min.
b. Find the linear speed of the sawteeth in ft/s.
2. The angle of elevation to the top of a very tall Building is found to be 15° from the ground at
a distance of 1 mi from the base of the building. Using this information, find the height of the
building (Round your answer to the nearest foot.)
3.
Find the exact value of the trigonometric functions
a. csc
11
3
b.
1
  7 
tan 

 6 
Final Exam
Math110
4. The terminal point P
tan t.
Sample
1,1 determined by a real number t is given. Find sin t, cos t, and
5. Find the domain and range for the trigonometric functions below:
Function
Domain
y  sin x
y  cos1 x
y  tan 1 x
6. Find the exact value of
7 

cos tan 1 
24 

2
Range
Math110
7.
Final Exam
Sample
Solve the triangle below (round sides length to the nearest integer)
8. Two tugboats that are a = 115 ft. apart pull a barge, as shown. If the length of one cable
is b =204 ft. and the length of the other is c = 225 ft., find the angle formed by the two
cables. (Round your answer to the nearest degree.)
9.
Find the amplitude, period and phase shift of the function
3 

y  3 cos x  
4

3
Math110
10.
Given
Final Exam


y  2 csc 2 x  
2

Find the period and graph the function on the interval
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Sample
 , 
Math110
Final Exam
11.
Verify the identify:
csc x  sec x
 sin x  cos x
cot x  tan x
12.
Verify the identity:
1  cos 2x
 sin 2x
tan x
5
Sample
Final Exam
Math110
13. Given that
Find
sin  
sin(   )
14. Given that
tan   
a.
sin 2
b.
cos 2
1
,
10
Sample
in Quadrant I and
1

, and

2
3
6
.Find
cos   
3
, 
5
in Quadrant II.
Math110
15. Solve the equation
16. Solve the equation
Final Exam
2 sin 3x  1  0
Sample
,Where 0 ≤ x ≤ 2π
2 cos 2 x  cos x  1  0
on the interval
17. Find the rectangular coordinate for the point with polar coordinate
7
0  x  2
(2,
3
)
4
Final Exam
Math110
18.
Sample
Test the polar equation for symmetry with respect to the polar axis, the pole, and the
line  

2
r  3  2 cos 
Then graph the equation.
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Final Exam
Math110
19.
a.
u  3i  4 j , v  6i  j ,
uv
b.
uv
c.
uv
Given
d. Find the angle between
u
and
Sample
Find
v to the nearest degree
20. A pilot heads his jet due east. The jet has a speed of 475 mi/h relative to the air. The wind is
blowing due north with a speed of 35 mi/h. Find the true velocity of the jet as a vector, and
write the vector in terms of the vectors i and j. Then find the true speed in mi/h and the
direction of the jet. (Round your answer to the nearest integer.)
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