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Lesson 4.1 Radian & Degree Measure

Learn about radian and degree measures, explore different types of angles, and discover coterminal angles. Calculate arc length, circumference, and angular speed using formulas and conversion units.

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Lesson 4.1 Radian & Degree Measure

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  1. Lesson 4.1Radian & Degree Measure

  2. Parts and Types of Angles Terminal & Initial Positive & Negative Coterminal A positive and negative angle where 30o & ______ 120o & ______

  3. Investigate • Draw a circle and make up a number for the radius. • Estimate a sector where the arc length would be equal to the radius • Find the circumference of the circle. • Use the formula below to find the degree measure of the arc • Then, what is the measure of the central angle of your sector? • Write your results in the table:

  4. Radian The angle size when the arc length equals the radius of a circle Question: How many radians to equal 180o? 360o? Full revolution:

  5. Radian Measures The units of an angle are in degrees or radians Converting Units have to cancel

  6. Examples Sketch in standard position. Find 2 coterminal angles to

  7. Arc Length and Speed Units = radians Arc Length = Linear Speed = Speed = Distance over time Angular Speed =

  8. Example Find the angle in degrees 31 in. 12 in.

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