Online Trigonometry Tutoring: Radian and Degree Measures
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Learn about radian and degree from certified online trigonometry tutor.
Radian and Degree Measures
- Measure of an angle is determined by the amount of rotation from the initial side to the terminal side.
- Many mathematical calculations in Geometry use degrees to measure and calculate angles.
- Degree measures are used in many practical applications in building and architecture that use
A radian is the measure of a central angle q that intercepts an arc ‘s‘ equal in length to the radius ‘r‘ of the circle.
✓ Radian is the measure of an angle that, when drawn as a central angle of a circle, intercepts an arc whose length is equal to the length of the radius of the circle.
✓ Radian measure for a full circle is 2π
✓ In radians, one complete counterclockwise revolution is 2π
✓ Degrees are used to measure direction and angle size
✓ Full circle = 360°.
✓ in degrees, one complete counterclockwise revolution is 360°.
So, degree and radian measure are related by the equations.
360° = 2π radians and
180° = π radians
Converting from Degree to Radians = multiply by π/180
Convert 70 degrees to radians
Solution: 70 x π/180
= 70 x 3.14/180 (π = 3.14)
= 1.221 radians
Converting from Radians to Degrees = multiply by 180/π
Convert 14 radians to degrees
Solution: 14 × 180/π
= 14 × 180/3.14
= 802.54 degrees
Problem 1. Find the radian measure of 225° .
Problem 2. Express 1.6 radians to degrees.
Problem 3. Convert π/6 radians to degrees.
Problem 4. Convert 140° to radian measure.
- 5π/4 radians
- 2.44 radians
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