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6.1: Angle Measure

6.1: Angle Measure. TSW understand and be able to apply degree and radian measurements of angles, understand and be able to apply coterminal angles, understand and find arc lengths, and understand linear and angular speed at an 85% mastery level as demonstrated by discussion and practice.

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6.1: Angle Measure

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  1. 6.1: Angle Measure TSW understand and be able to apply degree and radian measurements of angles, understand and be able to apply coterminal angles, understand and find arc lengths, and understand linear and angular speed at an 85% mastery level as demonstrated by discussion and practice.

  2. Angle Measure Units of measurement: degrees and radians Conversion: Ex: Express 60o in radians. Ex: Express in degrees.

  3. Coterminal Angles Two angles are coterminal if their sides coincide. Ex: Find angles that are coterminal with the angle in standard position. Ex: Find angles that are coterminal with the angle in standard position. Ex: Find an angle with measure between 0o and 360o that is coterminal with the angle of measure 1290o in standard position.

  4. Length of a Circular Arc r = radius of a circle s = length of the arc Θin radians Ex: Find the length of an arc of a circle with radius 10 m that subtends a central angle of 30o. Ex: A central angle Θ in a circle of radius 4 m is subtended by an arc length of 6 m. Find the measure of Θ in radians.

  5. Area of a Circular Sector r = radius of a circle Θin radians Ex: Find the area of a sector of a circle with central angle 60o if the radius of the circle is 3 m.

  6. Circular Motion Θin radians s = arc length t = time Ex: A boy rotates a stone in a 3-ft-long sling at a rate of 15 revolutions every 10 seconds. Find the angular and linear velocities of the stone.

  7. Circular Motion Ex: A woman is riding a bicycle whose wheels are 26 inches in diameter. If the wheels rotate at 125 revolutions per minute (rpm), find the speed at which she is traveling, in mi/h.

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