Examination 2P - Valencia College
MAC 1114 Practice Test #2 Chapters 3-4. Lial
1. Convert 55° to radian angle. Your answer should be exact.
Answer: 11π/36
2. Convert the radian angle 1/9 to a degree measure. Your answer should be exact.
Answer: 20/π °
3. Find (without using a calculator) the exact value of: (use the concepts found in the Special Angles Radians link in the Practice Problems in BB
a) [pic] b) [pic] c) [pic] Answer: 0, ½, -[pic]
4. Use a proportion to find how many radians there are if the two hands of the clock are at 12:20? Answer: 11л/18 rad
5. A small wheel (radius 5m.) and a large wheel (radius 8m.) rotate at the same time. Through how many degrees will the large wheel rotate if the smaller one rotates through 160˚? Answer: 100°
6. An arc of length 2cm subtends an angle of л °. Find the exact length of the radius of the circle. Answer: 360/л2 cm.
7. Find the area of a sector with radius 6ft. and angle 30º.
Answer: 3л ft2
8. In the circle below, C is the center of the circle, and (BCD is a right angle subtended by the arc s from B to D. If the straight-line distance from B to D is 4 meters, what is the length the arc s?
Answer: [pic][pic]
9. Find the least positive value of x where the graph of [pic]crosses the x–axis. Show the graph. Answer: [pic]
10. (No Calculator) Sketch the graph [pic] for[pic]. Include all the coordinates of all maximum and minimum points. Label your asymptotes if any.
Check your answer by graphing with a calculator.
11. The graph pictured below has an equation of the form[pic] find a and b.
[pic]
Answer: a= - 6, b=1/2
12. The graph pictured below has an equation of the form[pic].
Find a, b and c. You can check your answer with your calculator.
[pic]
Answer: a=1, b=3, c=-π/4;
13. (No Calculator) Sketch one period of the graph of[pic]. Label your intercepts and asymptotes. Check your answer by graphing with a calculator.
14. (No Calculator) Sketch one period of the graph of[pic]. Label your intercepts and asymptotes. Check your answer by graphing with a calculator.
15. (No Calculator) List the period and phase shift for[pic].
Answer: P =2π, Shift = - π/2 (π/2 to the left)
16. (No Calculator) Complete the Following Table
|[pic] (270°) | | | |
| [pic] (180°) | | | |
|[pic] (90°) | | | |
|[pic] (60°) | | | |
|[pic] (45°) | | | |
|[pic] (30°) | | | |
|0 (0°) | | | |
|θ |sin θ |cos θ |tan θ |
17. Find the exact values for each trig function. Draw the reference triangle. Check your answers using your calculator.
a) sin (-5(/6) = b) cos (-7π/2) = c) tan(7π/3) =
d) cos (2(/3) = e) tan (7(/4) = f) tan (-3(/2) =
g) sec (2() = h) cot (-5(/3)= i) csc(7π/6)=
18. Suppose that point P is on a circle with radius 10 cm, and ray OP is rotating with angular velocity [pic] radian per second.
(a) Find the angle generated by P in 6 seconds.
Ans:[pic]rad.
(b) Find the distance traveled by P along the circle in 6 seconds
Ans: [pic] cm.
(c) Find the linear velocity of P
Ans: [pic]cm per second.
19. A belt runs a pulley of radius 6 cm at 80 revolutions per minute.
(a) Find the angular velocity of the pulley in radians per second.
Ans: [pic] rad/s
(b) Find the linear velocity of the belt in centimeters per second.
[pic]cm/s.
20. A satellite traveling in a circular orbit 1600 km above the surface of Earth takes two hours to make an orbit. Assume that the radius of Earth is 6400 km.
(a) Find the linear velocity of the satellite.
Ans: [pic] km/ hr.
(b) Find the distance traveled in 4.5 hours.
Ans: [pic]km.
21. If an alternating voltage E in an electrical circuit has an amplitude of 12 V at t =0 and a frequency of 40 Hz, Find the equation of the form[pic] that gives the voltage at any time t.
Ans: E=12 cos (80πt)
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