Coterminal Angles Degree and Radian Worksheet Quick Guide
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Coterminal Angles Degree and Radian Worksheet
Coterminal angles are angles that have the same initial and terminal sides but differ in their angle measures by a multiple of 360 degrees. In this worksheet, we will explore coterminal angles in both degrees and radians and practice finding coterminal angles for given angles.
Instructions:
1. Convert the given angle measure to its radian equivalent.
2. Find three coterminal angles for the given angle in degrees and radians.
3. Write the coterminal angles in both degrees and radians.
4. Check your answers using a calculator.
Example:
Given angle: 120 degrees
Radian equivalent: 120 degrees = 120 * pi / 180 = 2pi / 3 radians
Coterminal angles in degrees: 120 + 360 = 480 degrees, 120 – 360 = -240 degrees
Coterminal angles in radians: 2pi / 3 + 2pi = 8pi / 3 radians, 2pi / 3 – 2pi = -4pi / 3 radians
1. 45 degrees
Radian equivalent:
45 degrees = 45 * pi / 180 = pi / 4 radians
Coterminal angles in degrees:
45 + 360 = 405 degrees, 45 – 360 = -315 degrees
Coterminal angles in radians:
pi / 4 + 2pi = 9pi / 4 radians, pi / 4 – 2pi = -7pi / 4 radians
2. 210 degrees
Radian equivalent:
210 degrees = 210 * pi / 180 = 7pi / 6 radians
Coterminal angles in degrees:
210 + 360 = 570 degrees, 210 – 360 = -150 degrees
Coterminal angles in radians:
7pi / 6 + 2pi = 19pi / 6 radians, 7pi / 6 – 2pi = -5pi / 6 radians
3. 300 degrees
Radian equivalent:
300 degrees = 300 * pi / 180 = 5pi / 3 radians
Coterminal angles in degrees:
300 + 360 = 660 degrees, 300 – 360 = -60 degrees
Coterminal angles in radians:
5pi / 3 + 2pi = 11pi / 3 radians, 5pi / 3 – 2pi = -pi / 3 radians
4. 60 degrees
Radian equivalent:
60 degrees = 60 * pi / 180 = pi / 3 radians
Coterminal angles in degrees:
60 + 360 = 420 degrees, 60 – 360 = -300 degrees
Coterminal angles in radians:
pi / 3 + 2pi = 7pi / 3 radians, pi / 3 – 2pi = -5pi / 3 radians
5. 135 degrees
Radian equivalent:
135 degrees = 135 * pi / 180 = 3pi / 4 radians
Coterminal angles in degrees:
135 + 360 = 495 degrees, 135 – 360 = -225 degrees
Coterminal angles in radians:
3pi / 4 + 2pi = 11pi / 4 radians, 3pi / 4 – 2pi = -5pi / 4 radians
6. 180 degrees
Radian equivalent:
180 degrees = 180 * pi / 180 = pi radians
Coterminal angles in degrees:
180 + 360 = 540 degrees, 180 – 360 = -180 degrees
Coterminal angles in radians:
pi + 2pi = 3pi radians, pi – 2pi = -pi radians
7. 30 degrees
Radian equivalent:
30 degrees = 30 * pi / 180 = pi / 6 radians
Coterminal angles in degrees:
30 + 360 = 390 degrees, 30 – 360 = -330 degrees
Coterminal angles in radians:
pi / 6 + 2pi = 13pi / 6 radians, pi / 6 – 2pi = -11pi / 6 radians
8. 240 degrees
Radian equivalent:
240 degrees = 240 * pi / 180 = 4pi / 3 radians
Coterminal angles in degrees:
240 + 360 = 600 degrees, 240 – 360 = -120 degrees
Coterminal angles in radians:
4pi / 3 + 2pi = 10pi / 3 radians, 4pi / 3 – 2pi = -2pi / 3 radians
9. 315 degrees
Radian equivalent:
315 degrees = 315 * pi / 180 = 7pi / 4 radians
Coterminal angles in degrees:
315 + 360 = 675 degrees, 315 – 360 = -45 degrees
Coterminal angles in radians:
7pi / 4 + 2pi = 15pi / 4 radians, 7pi / 4 – 2pi = -pi / 4 radians
10. 360 degrees
Radian equivalent:
360 degrees = 360 * pi / 180 = 2pi radians
Coterminal angles in degrees:
360 + 360 = 720 degrees, 360 – 360 = 0 degrees
Coterminal angles in radians:
2pi + 2pi = 4pi radians, 2pi – 2pi = 0 radians
In this worksheet, we have practiced finding coterminal angles for given angles in both degrees and radians. Coterminal angles are important in trigonometry as they help simplify calculations and understand periodic functions better. Make sure to practice more problems to improve your understanding of coterminal angles and their applications in trigonometry.
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