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Angles and Radian Measure - Convert, Estimate, and Calculate

Learn how to estimate and convert angle measures between radians and degrees, find coterminal angles, determine linear speed and arc length on a circle. Practice with the unit circle and solve real-life problems involving circular motion.

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Angles and Radian Measure - Convert, Estimate, and Calculate

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  1. Angles and Radian Measure Section 4.1

  2. Objectives • Estimate the radian measure of an angle shown in a picture. • Find a point on the unit circle given one coordinate and the quadrant in which the point lies. • Determine the coordinates of a point on the unit circle given a point on the unit circle. • Find coterminal angles. • Convert angle measures between radians and degrees. • Determine the linear speed of an object traveling in a circular motion. • Determine the arc length on a given circle.

  3. Vocabulary • unit circle • radian measure of an angle (radians) • degrees • vertex of an angle • terminal side of an angle • initial side of an angle • linear speed (length per unit of time) • length of a circular arc • angular speed (radians per unit of time)

  4. Unit Circle

  5. Consider the picture below. The angle θ is an integer when measured in radians. Give the measure of the angle.

  6. Find an angle between 0 and 2π that is coterminal to the angle Coterminal Angles: Angles are coterminal if they are in standard position and have the same terminal side.

  7. Formulas • Conversion between degrees and radian • Length of a circular arc • Linear speed • Angular speed

  8. Find the degree measure of anangle with radian measure

  9. Find the radian measure of anangle with degree measure

  10. Find the length of the arc on a circle of radius r = 6 inches intercepted by a central angle θ = 135 degrees

  11. A Ferris wheel has a radius of 30 feet and is rotating at 3.5 revolutions per minute. Find the linear speed, in feet per minute, of a seat on the Ferris wheel.

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