일반각과 호도법

For the following exercises, convert the angle measures to radians.

Find the length of an arc in a circle of radius 7 meters intercepted by the central angle of $85^\circ .$

For the following exercises, convert the angle measures to radians.

Find the area of the sector of a circle with diameter 32 feet and an angle of $\frac{3\pi }{5}$ radians.

For the following exercises, draw the angle provided in standard position on the Cartesian plane.

Find the linear speed of a point on the equator of the earth if the earth has a radius of 3,960 miles and the earth rotates on its axis every 24 hours. Express answer in miles per hour. Round to the nearest hundredth.

For the following exercises, draw the angle provided in standard position on the Cartesian plane.

A car wheel with a diameter of 18 inches spins at the rate of 10 revolutions per second. What is the car's speed in miles per hour? Round to the nearest hundredth.

Explain the differences between linear speed and angular speed when describing motion along a circular path.

For the following exercises, use to given information to find the length of a circular arc. Round to two decimal places.

Find the length of the arc of a circle of diameter 14 meters intercepted by the central angle of $\frac{5\pi }{6}.$

For the following exercises, use to given information to find the length of a circular arc. Round to two decimal places.

Find the length of the arc of a circle of diameter 12 meters intercepted by the central angle is 63°.

For the following exercises, use the given information to find the area of the sector. Round to four decimal places.

A sector of a circle has a central angle of 45° and a radius 6 cm.

For the following exercises, use the given information to find the area of the sector. Round to four decimal places.

A sector of a circle has a central angle of 30° and a radius of 20 cm.

For the following exercises, use the given information to find the area of the sector. Round to four decimal places.

A sector of a circle with diameter 10 feet and an angle of $\frac{\pi }{2}$ radians.

For the following exercises, use the given information to find the area of the sector. Round to four decimal places.

A sector of a circle with radius of 0.7 inches and an angle of $\pi$ radians.

A truck with 32-inch diameter wheels is traveling at 60 mi/h. Find the angular speed of the wheels in rad/min. How many revolutions per minute do the wheels make?

A bicycle with 24-inch diameter wheels is traveling at 15 mi/h. Find the angular speed of the wheels in rad/min. How many revolutions per minute do the wheels make?

A wheel of radius 8 inches is rotating 15°/s. What is the linear speed $v,$ the angular speed in RPM, and the angular speed in rad/s?

A wheel of radius 14 inches is rotating 0.5 rad/s. What is the linear speed $v,$ the angular speed in RPM, and the angular speed in deg/s?

A computer hard drive disc has diameter of 120 millimeters. When playing audio, the angular speed varies to keep the linear speed constant where the disc is being read. When reading along the outer edge of the disc, the angular speed is about 200 RPM (revolutions per minute). Find the linear speed.

When being burned in a writable CD-R drive, the angular speed of a CD varies to keep the linear speed constant where the disc is being written. When writing along the outer edge of the disc, the angular speed of one drive is about 4,800 RPM (revolutions per minute. Find the linear speed if the CD has diameter of 120millimeters.

Find the distance along an arc on the surface of Earth that subtends a central angle of 5 minutes $\left(1\text{ minute}=\frac{1}{60}\text{ degree}\right)$. The radius of Earth is 3960 miles.

Find the distance along an arc on the surface of Earth that subtends a central angle of 7 minutes $\left(1\text{ minute}=\frac{1}{60}\text{ degree}\right).$ The radius of Earth is $3960$ miles.

Consider a clock with an hour hand and minute hand. What is the measure of the angle the minute hand traces in $20$ minutes?