Unit Circle
What are the coordinates of the point on the unit circle at 0°?
(1,0)
What is the standard form of a circle centered at the origin with radius 1?
x2+y2=1
What is π(pi) radians equal to in degrees?
180
What is the formula for arc length?
arc length(s) = θ x r
What is the reference angle for 150°?
30°
What is the y-coordinate of the point on the unit circle at 90°?
1
Rewrite the equation x2+y2=25 in general form
x2+y2−25=0
Convert 90° to radians.
π/2
Find the arc length of a circle with radius 4 and angle π/2.
2π
What is the reference angle for 210°?
30°
What is the cosine of 120° using the unit circle?
-1/2
What is the radius of the circle represented by x2+y2=49?
7
Convert 3π/4 to degrees.
135
A circle has a radius of 6 and an angle of 60°. What is the arc length? (Give in terms of π)
2π
Find the reference angle for 315°
45°
What is the sine value of 330°?
-1/2
A circle has the general form equation x2+y2+6x−8y+9=0. Rewrite this equation in standard form.
(x+3)2+(y−4)2=16
What is 5π/3 radians to degrees?
300
The arc length is 5π and the radius is 10. Find the angle in radians.
π/2
What is the reference angle for 5π/6?
π/6
Give the coordinates on the unit circle for 225°
-√2/2, -√2/2
The point (x,y)=(−3,4)(x, y) = (-3, 4)(x,y)=(−3,4) lies on a circle centered at the origin. Write the standard and general form of the circle’s equation, and state its radius.
standard: x2+y2=25
general: x2+y2−25=0
radius: 5
A circle has an angle of 7π/6. What is the degree measure and in which quadrant does it lie?
210, quadrant III
A wheel with radius 12 cm rolls out an arc of 8π cm. What angle did it rotate through, in degrees?
120°
If an angle is 11π/6, find its reference angle in degrees and radians.
π/6, 30°