Unit 1 test: Angles

Convert $210^\circ$ to radians. Give an exact answer in terms of $\pi$.

Convert $\dfrac{3\pi}{5}$ radians to degrees.

Convert $2.2$ radians to degrees. Round to the nearest tenth of a degree.

An angle in standard position measures $4$ radians. In which quadrant does its terminal side lie?

Find the angle between $0^\circ$ and $360^\circ$ that is coterminal with $1110^\circ$.

Find the angle between $0$ and $2\pi$ that is coterminal with $-\dfrac{11\pi}{4}$. Give an exact answer in terms of $\pi$.

Which pair of angles is coterminal?

Find the reference angle of $325^\circ$, in degrees.

Find the reference angle of $\dfrac{9\pi}{5}$. Give an exact answer in terms of $\pi$.

Find the reference angle of $-500^\circ$, in degrees.

A circle has radius $15$ cm. Find the exact length of the arc cut off by a central angle of $\dfrac{4\pi}{5}$, in centimeters. Give your answer in terms of $\pi$.

An arc of length $18$ inches lies on a circle of radius $4$ inches. Find the central angle in radians.

Find the exact area of a sector with radius $6$ m and central angle $120^\circ$, in square meters. Give your answer in terms of $\pi$.

A point on a spinning disk makes $5$ complete revolutions in $4$ seconds. Find its angular speed in radians per second. Give an exact answer in terms of $\pi$.

A wheel with radius $0.35$ m turns at $300$ revolutions per minute. Find the linear speed of a point on its rim in meters per second. Round to the nearest tenth.