TRIGONOMETRY CHAPTER 2 TEST
TRIGONOMETRY Review for CHAPTER 2 NAME:
Change each of the following to radian measurements (keep in π form).
Show your work. ( 1pt each)
1) - 275 = _____________
2) 150 = _____________
3) 2/5 rotation, counter clockwise = _______________
4) 2/3 rotation, clockwise = ____________________
Solve each of the following. Be sure to show your work.
5) On a circular platform of a merry go round that rotates 8 rpm, point P represents the location of a particular horse that is 6 meters from the center. Find the angular speed of the merry go round in radians per second.
6) Using the merry go round from the above problem, find the linear speed traveled by the horse at point P.
7) In a circle O with radius 6 meters, central angle POQ intersects arc PQ. Find, to the nearest tenth, the radian measure of angle POQ if the length of arc PQ is 32 meters.
In the lines provided, name the amplitude, period, horizontal center and phase shift for each of the following. (1 pt each)
8) y = - 3 sin 2x + 4 amplitude = ____________
period = ______________
vertical shift = _____________
phase shift = _________________
9) y = 3 cos ( x + π ) +2 amplitude = ____________
period = ______________
vertical shift = _____________
phase shift = _________________
10) y = 5 cos 3 x – 6 amplitude =_____________
period = _______________
vertical shift = _____________
phase shift = __________________
Write the equation containing sin(x) that satisfies the given information:
11) Amplitude = 8 Period = 4 π Vertical shift = down 2 y = _______________________
Match the equations to their characteristics. Place the letter of the matching equation on the blank before its characteristic:
A). y = 2 sin 2(x – π/2) + 4
B). y = 2 sin (4x + 2 π) + 4
C). y = sin (x + π/4)
D). y = sin ( x – π/4)
E). y = 2 sin (x – π) + 4
Amplitude Period Phase shift Vertical shift
12) _____ 1 2π π/4 units left none
13) _____ 2 2π π units right up 4
14) _____ 1 2 π π/4 units right none
15) _____ 2 π π/2 units right up 4
16) _____ 2 π/2 π/2 units left up 4
Graph at least one cycle of each of the following:
17) y = cos (2θ)
[pic]
18) y = 3 sinθ + 1
[pic]
19) . y = sin (θ – [pic])
[pic]
20) y = 3 sec(θ )
[pic]
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