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5.1 Angles and Radian Measure

5.1 Angles and Radian Measure. ANGLES. Ray – only one endpoint Angle – formed by two rays with a common endpoint Vertex – the common endpoint of an angle’s initial and terminal sides. -Vertex @ origin -Initial side lies along positive x-axis. QUADRANTS.

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5.1 Angles and Radian Measure

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  1. 5.1 Angles and Radian Measure

  2. ANGLES • Ray – only one endpoint • Angle – formed by two rays with a common endpoint • Vertex – the common endpoint of an angle’s initial and terminal sides. -Vertex @ origin -Initial side lies along positive x-axis

  3. QUADRANTS When in standard position, an angle’s terminal side lies in a quadrant.

  4. Quadrantal Angle Not in a quadrant. Terminal side is on either the x- or y-axis.

  5. MEASURING ANGLES USING DEGREES • Acute • Right • Obtuse • Straight

  6. MEASURING ANGLES IN RADIANS • One radian is the measure of the central angle of a circle that intercepts an arc equal in length to the radius of the circle.

  7. Ex #1: RADIAN MEASURE • ϴ = • A central angel, ϴ, ina circle of radius 12 feet intercepts an arc of length 42 feet. What is the radian measure of ϴ?

  8. MEASURING ANGLES IN RADIANS • One radian is the measure of the central angle of a circle that intercepts an arc equal in length to the radius of the circle.

  9. Plus just a little bit more!

  10. Radians and Degrees Ifϴ = what is the angle of the entire circle? REMEMBER: Circumference = 2πr

  11. CONVERSION • Degrees  Radians Degrees * • Radians  Degrees Radians *

  12. Ex #2-3 • CONVERT TO RADIANS: • CONVERT TO DEGREES: • radians • radians • radian

  13. Drawing Angles in Standard Position • Ex #4: Draw the following angles

  14. Drawing Angles in Standard Position • Ex #4: Draw the following angles

  15. UNIT CIRCLE

  16. FINDING COTERMINAL ANGLES NOTICE: YOUR BOOK ASKS FOR POSITIVE ANGLES LESS THAN 360

  17. HOMEWORK • Pg. 480 #1-55 odd + pg. 476 Checkpoint #5 (you’ll need to read Example 5 in order to do the checkpoint)

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