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Radian Measure That was easy
What does that mean? One radian is the measure of a central angle of a circle that intercepts an arc whose length equals a radius of the circle. Central angle intercepts an arc whose length, s, is inches in a circle that has a radius length of 12 inches. Find r = 12 General Formula or or That was easy
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Converting from Degrees to Radians
To change from degrees to radians, multiply the number of degrees by Convert the following angle measurements from degrees to radians.
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Converting from Radians to Degrees
To change from radians to degrees, multiply the number of radians by Convert the following angle measurements from radians to degrees.
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Comparing Degrees and Radians
The radius of a circle is 12 centimeters. What is the number of centimeters in the length of the minor arc intercepted by a central angle that measures 135o? Method 1 Method 2 r = 12 s How about that. You get the same answer either way.
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Homework Page : 4 – 22 Even Numbers
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Angles in Standard Position
Let’s look at a diagram that will explain what an angle in standard position is. y If the terminal side rotates in a counterclockwise direction, the angle is positive. Terminal Side -x x Initial Side If the terminal side rotates in a clockwise direction, the angle is negative. -y
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Drawing Angles in Standard Position
Draw the following angles. 360o 180o 270o
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Reference Angles The reference angle is the acute angle whose vertex is the origin and whose sides are the terminal side of the original angle and the x-axis. The reference angle is denoted as Quadrant I Quadrant II Quadrant III Quadrant IV
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Finding Reference Angles
For each angle given in radian measure, find the measure of the reference angle in radians. That was easy
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Coterminal Angles A positive angle and a negative angle are coterminal angles if the sum of the absolute values of their degree measures is 360 or a multiple of 360. y Example 1 A rotation angle measures 210o. What is the measurement of its coterminal angle? -x x Example b A rotation angle measures 300o. What is the measurement of its coterminal angle? -y
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Also name the Coterminal Angle for each angle
Homework Page 405: All Also name the Coterminal Angle for each angle
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Comparing Degrees and Radians
The radius of a circle is 12 centimeters. What is the number of centimeters in the length of the minor arc intercepted by a central angle that measures 135o? Method 1 Method 2 r = 12 s How about that. You get the same answer either way.
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Arc Length and Radians
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Homework Page 405: 28 – 40 Even Numbers
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