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Angles and Radian Measure

Angles and Radian Measure. Alg ll/Trig – Trig Ch C day 2. Notice that the graphs of sine, cosine and tangent repeat. Because these functions “repeat” we say they are __________ Sine repeats every ____  . Sine has a ________of _____ 

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Angles and Radian Measure

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  1. Angles and Radian Measure Alg ll/Trig – Trig Ch C day 2

  2. Notice that the graphs of sine, cosine and tangent repeat. Because these functions “repeat” we say they are __________ Sine repeats every ____. Sine has a ________of _____  Cosine repeats every ____. Cosine has a _______ of ____  Tangent repeats every ____. Tangent has a ________ of ____  Find the period for each of the following functions: PERIODIC 360 PERIOD 360 360 PERIOD 360 PERIOD 180 180 y = sec xy = csc x y = cot x 360 180 360

  3. Radian Measure Consider an angle such that its vertex is at the center of a circle. Let r= _________ and S be the _________ of the arc created by the angle . We will no longer measure angles in __________. They will now be measured in ________ defined as such: RADIUS LENGTH DEGREES RADIANS In other words,  is the number of _______that make up the ______ that  creates. This means that the radian measure of an angle is simply a __________ of the _________________ of the circle. RADII ARC FRACTION CIRCUMFERENCE

  4. 1 Revolution: ¾ Revolution:

  5. ½ Revolution: ¼ Revolution:

  6. Conversion Formulas: Radians  Degrees: Degrees  Radians: Multiply by ___________ Multiply by ___________ Change in degrees Change 32 into radians.

  7. What is the formula for the rate (or speed) at which an object is moving? Linear Speed When an object is moving at a constant speed in a ____________ path with a radius of, r, the linear speed of the object is given by _______________, which is just ________________. Angular Speed The angular speed of the object is the measure of how ______ the _______ of _________ for the object _________ and is given by _________, where  is an angle measure in ________ and t is _______. CIRCULAR FAST ROTATION ANGLE CHANGES RADIANS TIME

  8. Example 3: A weather satellite orbits the Earth at an altitude of approximately 22,200 miles above Earth’s surface. The radius of the Earth is 3960 miles. If the satellite observes a fixed region on Earth and has a period of revolution of 24 hours, what is the linear speed of the satellite? What is its angular speed? linear speed angular speed satellite Earth Time: 24 hours Radius: 26,160 miles 3960 + 22,200 LINEAR SPEED: ANGULAR SPEED:

  9. ( , ) (0 , 1) ( , ) 90 ( , ) ( , ) ( , ) 120 60 ( , ) 135 45 150 30 (-1, 0) (1, 0) 0 180 360 210 330 225 315 ( , ) 240 300 ( , ) ( , ) ( , ) ( , ) 270 ( , ) (0, -1)

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