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Angles and Radian Measure

Learn how to estimate and convert radian measures, find points on the unit circle, determine angular and linear speeds, and calculate arc lengths. Practice with coterminal angles and explore formulas for conversions and circular motion.

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Angles and Radian Measure

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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 2 minutes. Find the linear speed, in feet per minute, of a seat on the Ferris wheel.

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