삼각함수 전체 문제

Find the area of a triangular piece of land that measures 110 feet on one side and 250 feet on another; the included angle measures 85°. Round to the nearest whole square foot.

Find the area of a triangle with sides of length 8.3, 6.6, and 9.1.

A pilot flies in a straight path for 2 hours. He then makes a course correction, heading 15° to the right of his original course, and flies 1 hour in the new direction. If he maintains a constant speed of 575 miles per hour, how far is he from his starting position?

Given ${z}_{1}=8\mathrm{cis}(36^\circ )$ and ${z}_{2}=2\mathrm{cis}(15^\circ ),$ evaluate each expression.

A ball is launched with an initial velocity of 95 feet per second at an angle of 52° to the horizontal. The ball is released at a height of 3.5 feet above the ground.

• ⓐFind the parametric equations to model the path of the ball.
• ⓑWhere is the ball after 2 seconds?
• ⓒHow long is the ball in the air?

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?