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Unformatted text preview: Math 111 Final Exam 1. In the given right triangle and . Find the length of leg a.
c (a) (b) b=9 (c)
62° (d) (e) (f) (Drawing not to scale) 2. Use fundamental identities and/or the complementary angle theorem to find the value of the
(a) 1 (b) (c) (d) (e) (f) 3. A straight trail leads up to an overlook. At the end of the trail, the elevation
is 0.8 miles higher than at the beginning of the trail. The inclination (grade)
of the trail is 13°. What is the length of the trail in miles?
(a) mi. (b) mi. (c) (d) mi. (e) mi. (f) 13° (Drawing not to scale) mi.
mi. 4. Given the following triangle, find the measure of the missing side length x.
Simplify where possible.
x (a) (b) #3 x .8 130° 3 #4 20° (c) (Drawing not to scale) (d) (e) (f) 5. Scott is trying to make a triangle with sides a, b, and c so that
How many triangles does the given information produce? (assume that in this triangle, side a
opposite of angle A, side b is opposite of angle B, and side c is opposite of angle C)
(a) No triangles
(d) None of these (b) One triangle
(c) Two triangles
(e) Not enough information to tell 6. Given the following triangle, find the measure of the missing side length x.
Simplify where possible.
(a) (b) (c) (d) (e) (f) #6 10°
x (Drawing not to scale) 5 7. Given the following triangle, use the law of cosines to find the measure
of the missing angle . Simplify where possible.
(a) (b) (c) (d) #7 8 (e) none of these 6 (Drawing not
to scale) 8. Sam is trying to build a triangular cage for her new baby hamster. She knows that hamsters
prefer 120° angles (don’t ask how she knows this, she’s just smart like that), so she wants to
make one of the angles in her triangular cage 120°. If the sides forming this 120° angle are 4 ft.
long and 1 ft. long, how long is the third side of the cage? (See the picture)
1 ft. 120° (b) ft. (b) ft. (c) 4 ft. #8 x ft. (Drawing not to scale) (d) ft. (e) ft. (f) ft. 9. Find the area of the hamster cage described and shown in the previous problem (#8).
(a) (b) (c) (d) (e) (f) 10. Find the area of a triangle with side lengths 7 miles, 12 miles, and 13 miles.
(a) (b) (c) (d) (e) (f) none of these 11. An old fashioned metronome is used to keep time for Tom as he plays the piano. A
weight at the end of the arm of the metronome is oscillating under simple harmonic motion.
At the rate it is beating, it takes 3 seconds for the weight to go back and forth once (one full
oscillation). The weight is 2 inches away from the center rest position at its farthest point.
Write an equation that relates the horizontal displacement of the weight from its rest
position at any given time t (in seconds).
(a) (b) (c) (d) 12. An object with a mass of 14 kilograms is attached to the end of a coil spring and is pulled
down a distance of 17 m. from its rest position and then released. There is a damping factor of
.7 kilograms/second. Assume that the positive direction of motion is up and the object takes 5
seconds to go one full oscillation (under simple harmonic motion). Write an equation that relates
the displacement d(t) (in meters) of the object from its rest position after t seconds.
(a) (b) (c) (d) 13. Sketch the graph of the following damped vibration curve:
1 1 /2 /2 -1 -1 (c) (d)
1 1 2 /2 4
-1 -1 14. Which of the following polar coordinates describe the same point as the point
in polar coordinates.
(a) (b) (c) (d) given (e) 15. Which of the following are rectangular coordinates of the point whose polar coordinates are
(a) (b) (c) (d) (e) 16. Convert the following equation from an equation using polar coordinates to an equation
using rectangular coordinates:
(d) none of these 17. Identify the graph of the following polar equation:
(a) (b) (c) (d) (e) (f) 18. Identify the graph of the following polar equation:
(a) (b) (c) (d) (e) (f) 19. If
(leave your answer in polar form). (a)
(c) are complex numbers, find the (b) 1
(d) 20. Using De Moivre’s Theorem, identify the complex number
written in the standard rectangular form
(a) (b) (c) (d) (e) Answers:
20. E ...
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This note was uploaded on 10/24/2011 for the course MATH 111 taught by Professor Stuff during the Fall '11 term at BYU.
- Fall '11