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Angles and Radian Measure

Angles and Radian Measure. Trigonometry, 1.0: Students understand the notion of angle and how to measure it, in both degrees and radians. They can convert between degrees and radians.

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Angles and Radian Measure

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  1. Angles and Radian Measure Trigonometry, 1.0: Students understand the notion of angle and how to measure it, in both degrees and radians. They can convert between degrees and radians. Trigonometry 2.0: Students know the definition of sine and cosine as y- and x-coordinates of points on the unit circle and are familiar with the graphs of the sine and cosine functions.

  2. Objectives • Students will be able to manipulate a unit of measure from radian to degree and vice versa. • Students will be able to solve for the length of an arc given the measure of the central angle. • Students will be able to calculate the area of a sector.

  3. Objective 1: Radians and Degrees Changing Radians to Degrees Changing Degrees to Radians • For every 1 radian you have approximately 57.3 which is equivalent to • Thus, we multiply our radians by to convert to degrees. • For every 1 degree you have approximately 0.17 radians which is equivalent to • Thus, we multiply our degrees by to convert to radians.

  4. Examples 1 Change 240 to radian measure in terms of . Change radians to degree measure.

  5. Examples 1 Change 240 to radian measure in terms of . Change radians to degree measure. 240 =240 =

  6. Examples 1 Change 240 to radian measure in terms of . Change radians to degree measure. 240 =240 = = =135

  7. Objective 2: Arc Length • Length of an arc, • r, represents the radius of your circle • , represents the radians of your central angle in the unit circle • Step 1: Change measure of central angle to radians • Step 2: Use radius given to find the length of the arc by using the formula above

  8. Examples 2 Given a central angle of 225, find the length of its intercepted arc in a circle of radius 4 centimeters. Round to the nearest tenth.

  9. Examples 2 Given a central angle of 225, find the length of its intercepted arc in a circle of radius 4 centimeters. Round to the nearest tenth. First, convert the measure of the central angle from degrees to radians. 225 = 225 = Then, find the length of the arc. s = r s = 4 s= 15.70796327 Use a calculator. The length of the arc is about 15.7 centimeters.

  10. Objective 3: Area of a Sector • Area of a Circular Sector, • r, represents the radius of your circle • , represents the radians of your central angle in the unit circle

  11. Examples 3 Find the area of a sector if the central angle measures radians and the radius of the circle is 12 centimeters. Round to the nearest tenth.

  12. Examples 3 Find the area of a sector if the central angle measures radians and the radius of the circle is 12 centimeters. Round to the nearest tenth. A = A = A 263.8937829 The area of the sector is about 263.9 square centimeters.

  13. Closing Remarks Summary Homework • What three things did you learn today? • Earth rotates on its axis once every 24 hours. What is the time, in hours, it will take for the Earth to rotate through an angle of 300 degrees? • 6.1 Angles and Radian Measure pg348#(17-51 odd, 53-55 EC). • Problems not finished will be left as homework.

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