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Understanding Degrees, Radians, and Angular Speed: A Comprehensive Guide

This guide provides students with essential concepts related to degrees, radians, and angular speed. It covers how to convert between degrees and radians, identify complementary and supplementary angles, and calculate coterminal angles. Additionally, it explains how to find the arc length of a circle given a central angle and how to determine linear and angular speed. Students are encouraged to use their notes to complete homework tasks that involve finding angle measures, implementing trigonometric definitions, and analyzing functions' domains.

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Understanding Degrees, Radians, and Angular Speed: A Comprehensive Guide

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  1. Students, Take out your calendar and your homework. Take out your spiral notebook and Complete the DNA.Use your notes if necessary. 3) Write the degree measure of each radian measure. Find a positive coterminal angle and a negative coterminal angle for the given angle.

  2. Supplementary Angles: measures add up to 180°. Complementary Angles: measures add up to 90°. • Complementary and supplementary angles must be positive. 1) Find the complement of each angle. 2) Find the supplement of each angle.

  3. 1. To convert degrees to radians, multiply degrees by 2. To convert radians to degrees, multiply radians by

  4. Rewrite each degree measure in radians and each radian measure in degrees. • In which quadrant does the terminal side of each angle lie?

  5. 1) A circle has a radius of 27 inches. Find the length of the arc intercepted by a central angle of 160°.

  6. Linear and Angular Speed • 2) The circular blade on a saw rotates at 2400 revolutions per minute. • Find the angular speed in radians per second. • The blade has a radius of 4 inches. Find the linear speed of a blade tip in inches per second.

  7. Definition of Trigonometric Functions Let t be a real number and let (x, y) be the point on the unit circle corresponding to t.

  8. Determine the exact values of the six trigonometric functions of the angle θ.

  9. Linear and Angular Speed • 2) The circular blade on a saw rotates at 2400 revolutions per minute. • Find the angular speed in radians per second. • The blade has a radius of 4 inches. Find the linear speed of a blade tip in inches per second.

  10. Find the domain of the following functions.

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