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Angles and Their Measure

Explore angles, their measurement, terminal sides, initial sides, vertices, and standard positions. Learn about positive and negative angles, quadrantal angles, measuring angles in radians and degrees, converting between degrees and radians, and finding coterminal angles. Practice drawing angles and conversions to deepen your understanding.

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Angles and Their Measure

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  1. Angles and Their Measure Section 13-2

  2. Angles Terminal Side Initial Side Vertex

  3. Standard Position: Initial side is on the positive x-axis with the vertex at the origin. Positive angles are measured counter-clockwise. Negative angles are measured clockwise. Positive Angle Negative Angle Quadrantal Angle: Angle in standard position with terminal side on an axis

  4. Measuring Angles There are two ways to measure angles: • Radians (One Circle = 2 radians) • Radians are the commonly used angle measure for Trig • Degrees (One circle = 360o)

  5. Ex: Draw each angle with the given measure in standard position 1. 215o 2. 3. -305o 4.

  6. Converting • If 360o = 2 radians, then 180o =  rad • To convert degrees to rad, use the ratio • To convert rad to degrees, use the ratio Ex: Convert 1. 45o to rad 2. to degrees

  7. Coterminal Angles • Two angles in standard position that have the same terminal side Ex: Find one positive angle and one negative angle that are coterminal with To find coterminal angles, add or subtract any number of full circles:

  8. HW: p.862 (3 – 31, 39 – 41)

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