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7.1E: Angles (Exercises)

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

    1. \(\frac{\pi}{4}\)

    2. \(-\frac{5 \pi}{3}\)

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

    3. \(-210^{\circ}\)

    4. \(180^{\circ}\)

    5. Find the length of an arc in a circle of radius 7 meters subtended by the central angle of \(85^{\circ}\).

    6. 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, find the angle between \(0^{\circ}\) and \(360^{\circ}\) that is coterminal with the given angle.

    7. \(420^{\circ}\)

    8. \(-80^{\circ}\)

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

    9. \(-\frac{20 \pi}{11}\)

    10. \(\frac{14 \pi}{5}\)

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

    11. \(-210^{\circ}\)

    12. \(75^{\circ}\)

    13. \(\frac{5 \pi}{4}\)

    14. \(-\frac{\pi}{3}\)

    15. 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.

    16. 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.

    This page titled 7.1E: Angles (Exercises) was last modified on Thu, 26 Dec 2024 22:30:56 GMT and is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform.

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