Angles on the Unit Circle
What is the angle in degrees for π/2 radians?
90°
A Ferris wheel makes one complete rotation in 60 seconds. What is the angular speed in degrees per second?
6 degrees per second
What are the coordinates of π/6?
(√3/2, 1/2)
Solve for sinθ if θ = 30°
sinθ = 1/2
In which quadrant is 120° located?
Quadrant II
Convert 300° to radians.
5π/3
A point moves around the unit circle at a constant speed. If it completes one rotation in 2 seconds, what is its angular speed in radians per second?
π radians per second
What are the coordinates of π/2?
(0,1)
Solve for cosθ if θ = 120°
cosθ = -1/2
In which quadrant is 225° located?
Quadrant III
What is the reference angle of 210°?
30°
The height of a point on a Ferris wheel follows a sine function. If the maximum height is 50 meters, and the minimum is 10 meters, what is the amplitude of the sine function?
20 meters
What are the coordinates of 3π/4?
(-√2/2, √2/2)
Solve for tanθ if θ = 225°
tanθ = 1
In which quadrant is 11π/6 located?
Quadrant IV
What is the radian measure of the angle that corresponds to -90°?
-π/2
A pendulum swings back and forth, and its position is modeled by x(t)= cos(2πt), where is time in seconds. What is the period of the motion?
1 second
What are the coordinates of 11π/3?
(1/2, -√3/2)
Solve for cotθ if θ = 5π/3
cotθ = -√3
In which quadrant is 3π/2
Quadrant III
Convert -7π/6 into degrees.
-210°
A wheel of radius 2 meters rotates at 10 revolutions per minute. What is the linear speed of a point on the edge of the wheel in meters per second?
20π over 60 or approximately 2.09 meters per second.
What are the coordinates of 19π/6?
(-√3/2, -1/2)
Solve for secθ if θ = 7π/6
secθ = -2√3/3
In which quadrant is 315° located?
Quadrant IV