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5-1 Angles and Degree Measure

5-1 Angles and Degree Measure. Give the angle measure represented by each rotation. 5.5 rotations clockwise 3.3 rotations counterclockwise. Coterminal Angles. Two angles in standard position having the same terminal side. θ + 360k°.

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5-1 Angles and Degree Measure

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  1. 5-1 Angles and Degree Measure

  2. Give the angle measure represented by each rotation. • 5.5 rotations clockwise • 3.3 rotations counterclockwise

  3. Coterminal Angles Two angles in standard position having the same terminal side. θ + 360k°

  4. Identify all angles that are coterminal with each angle. Then find one positive angle and one negative angle that is coterminal with the angle. • 45° b) 225°

  5. If each angle is in standard position, determine a coterminal angle that is between 0° and 360°. State the quadrant in which the terminal side lies. • 775° • -1297°

  6. Reference Angle Rule The acute angle to the x-axis.

  7. Find the measure of the reference angle for each angle. • 120° • -135°

  8. Degrees Minutes and Seconds The concept of degree measurement is rooted in the ancient Babylonian culture. The Babylonians based their number system on 60 rather than 10 as we do today. In an equilateral triangle, they assigned the measure of each angle to be 60.

  9. Therefore, one sixtieth (1/60) of the measure of the angle on an equilateral triangle was equivalent to one unit or degree (1°). The degree is subdivided into 60 equal parts known as minutes (1’) and the minute is subdivided into 60 equal parts known as seconds (1”).

  10. So 1° = 60’ 1’ = 60”

  11. Change 39°5’34” to decimal form to the nearest thousandth. Change 15.735° to degrees, minutes and seconds.

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