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Section 13.2: Angles and Angle Measure

Section 13.2: Angles and Angle Measure. CP Algebra II. Angles in Standard Position. An angle is considered to be in standard position when its vertex is at the origin, its initial side is on the positive x-axis and the ray that rotates about the center is called the terminal side.

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Section 13.2: Angles and Angle Measure

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  1. Section 13.2: Angles and Angle Measure CP Algebra II

  2. Angles in Standard Position • An angle is considered to be in standard position when its vertex is at the origin, its initial side is on the positive x-axis and the ray that rotates about the center is called the terminal side.

  3. Angle Measurement • If the terminal side travels counterclockwise, the angle is said to have positive measure. • If the terminal side travels clockwise, the angle is said to have negative measure.

  4. Example • Draw an angle with the given measure in standard position.

  5. Coterminal Angles • Two or more angles in standard position with the same terminal side are called coterminal angles.

  6. How to Find Coterminal Angles • Coterminal angles always differ by • You will be asked to find a coterminal with positive measure and a coterminal with negative measure. • By looking at the measure of the given angle, you decide which of the options on the next slide you will use to find the proper coterminal angles.

  7. How to Find Coterminal Angles • If the angle measure is between and , subtract once to find a negative coterminal. Then add once to the original angle measure to find a positive coterminal. • If the angle measure is between and , subtract once to find a negative coterminal. Then add once to the original angle measure to find a positive coterminal.

  8. If the angle measure is greater than , subtract until you find a negative coterminal. The last positive angle measure you have is a positive coterminal. (If smaller than , add instead)

  9. Examples • Find a negative and positive coterminal angle for each of the following.

  10. How Angles are Measured • There are three angle measurements that are popular: • Degrees – from geometry • Degree, Minute, Second – used in navigation • Radians – new to you and highly used in precalc/analysis, calculus and CP Algebra II

  11. Radians • Radian angle measure is a way to measure angles using the arc length of a circle. • In case geometry has escaped you: • To find the arc length using a central angle (in radians) and the radius of a circle r, the arc length s is defined as

  12. Converting Radians into Degrees and Vice Versa • How many radians are there in a circle? • How many radians are there in half a circle?

  13. Conversion Formulas • Degrees to Radians: Multiply by • Radians to Degrees: Multiply by

  14. Conversion Examples • Convert to radians or degrees. • Although you do have conversion formulas, when given radians in a problem after this section, you MUST use the radian angle measure.

  15. Homework • Section 13.2: pg. 821 (19-30, 33, 34)

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