Degrees, Radians, and the Unit Circle Practice

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Designed for 11th grade pre-calculus and trigonometry students. Solve each problem showing exact values in terms of pi unless asked for a rounded decimal.

Convert 45 degrees to radians in simplest terms with pi.
Convert 210 degrees to radians in simplest terms with pi.
Convert 5 * pi / 3 radians to degrees.
Find a positive coterminal angle between 0 and 2 * pi for the angle -pi / 4.
Find a coterminal angle between 0 and 360 degrees for 420 degrees.
A circle has a radius of 10 cm. Find the arc length intercepted by a central angle of 2 * pi / 5 radians.
A pizza has a radius of 8 inches. What is the area of a slice with a central angle of pi / 4 radians?
Convert -120 degrees to radians and identify which quadrant its terminal side lies in.

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Degrees, Radians, and the Unit Circle Practice

Answer key

Convert 45 degrees to radians in simplest terms with pi.
pi / 4 radians
Convert 210 degrees to radians in simplest terms with pi.
7 * pi / 6 radians
Convert 5 * pi / 3 radians to degrees.
300 degrees
Find a positive coterminal angle between 0 and 2 * pi for the angle -pi / 4.
7 * pi / 4 radians
Find a coterminal angle between 0 and 360 degrees for 420 degrees.
60 degrees
A circle has a radius of 10 cm. Find the arc length intercepted by a central angle of 2 * pi / 5 radians.
4 * pi cm (approximately 12.57 cm)
A pizza has a radius of 8 inches. What is the area of a slice with a central angle of pi / 4 radians?
8 * pi square inches (approximately 25.13 sq in)
Convert -120 degrees to radians and identify which quadrant its terminal side lies in.
-2 * pi / 3 radians (or coterminal 4 * pi / 3 radians); Quadrant III