일반각과 호도법

For the following exercises, find the angle between 0° and 360° that is coterminal to the given angle.

−110°

For the following exercises, find the angle between 0° and 360° that is coterminal to the given angle.

700°

For the following exercises, find the angle between 0° and 360° that is coterminal to the given angle.

1400°

For the following exercises, find the angle between 0 and $2\pi$ in radians that is coterminal to the given angle.

$-\frac{\pi }{9}$

For the following exercises, find the angle between 0 and $2\pi$ in radians that is coterminal to the given angle.

$\frac{10\pi }{3}$

For the following exercises, find the angle between 0 and $2\pi$ in radians that is coterminal to the given angle.

$\frac{13\pi }{6}$

For the following exercises, find the angle between 0 and $2\pi$ in radians that is coterminal to the given angle.

$\frac{44\pi }{9}$

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.

A person is standing on the equator of Earth (radius 3960 miles). What are their linear and angular speeds?

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?

Two cities have the same longitude. The latitude of city A is 9 degrees north and the latitude of city B is 30 degree north. Assume the radius of the earth is 3960 miles. Find the distance between the two cities.

A city is located at 40 degrees north latitude. Assume the radius of the earth is 3960 miles and the earth rotates once every 24 hours. Find the linear speed of a person who resides in this city. Refer to Unit Circle: Sine and Cosine Functions for information on trigonometric functions.

A city is located at 75 degrees north latitude. Assume the radius of the earth is 3960 miles and the earth rotates once every 24 hours. Find the linear speed of a person who resides in this city. Refer to Unit Circle: Sine and Cosine Functions for information on trigonometric functions.