Angle Conversions
Trig ratio values
Of or relating to arc length
Linear speed
Angular speed
100
Convert 60 degrees to radians
pi over 3
100
Use a calculator to approximate sin 2.203
.8063
100
Find the exact value of s in quadrant 1 if cos s = (1/2) Express your answer in radians
π/3
100
Find v if s = 57 meters and t = 3 seconds (This is my top speed.)
v = 19 m/s
100
Find ω if Θ = π/6 and t = 1 sec
ω = π/6 radians/s
200
Convert 240 degrees to radians
2 pi over 3
200
Use a calculator to approximate csc .5291
.5047
200
Find the exact value of s in quadrant II if cos s = -(1/2). Express your answer in radians.
2π/3
200
Find v if r = 6 cm, Θ = 3π/4, and t = 0.5 s
v = 9π cm/s
200
Find ω if Θ = 11π/6 and t = 3 sec
ω = 11/18 radians per second or 198 radians per second
300
Convert 5π/3 to degrees
300 degrees
300
Find the exact value of cos (4π/3)
-(1/2)
300
Use a calculator to find the value of s in cot s = 2.1925
s = .0079
300
Find v if r = 4.8 mm and ω = 6 revolutions per 4 minutes
v = 14.4π mm/minutes
300
Find ω if v = 24 m/s and r = 6 m
Θ = 4 radians/s
400
Convert 630 degrees to radians
7π/2
400
What is the exact value of cot (7π/6)
The square root of 3
400
Find s if r = 190 and Θ = 2π/15
s = 76π/3
400
A gear is being turned by a chain at 36 revolutions per minute. If the radius of the gear is 20π/3, then what is its linear velocity.
8 m/s
400
Find ω if s = 40 meters, t = 10 seconds, and r = 4 meters
ω = 1 radian
500
Convert 20π/6 to degrees.
600 degrees
500
Find the exact value of sec (-5π/6)
Negative 2 root 3 over 3
500
A smaller wheel (r = 3.5) is rotating against a larger wheel (r = 32). Through how many degrees will the larger wheel rotate if the smaller one rotates 720 degrees.
39.375 degrees
500
Find Θ if v = 16 m/s, r = 22/3 m, and t = 13 s
Θ = 208/11
500
Two pulleys with radii measuring 16 meters and 1.5 meters are connected by a belt. The larger pulley rotates at 240π radians per minute. Find the linear velocity and angular velocity of the smaller pulley. Leave answers in terms of π.
v = 3840 π meters/minute ω = 2560 π radians/minutes
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