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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

\theta = \frac{s}{r}  = \frac{length of subtendedarc}{length of radius}

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

Example 1

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.

Answer Key
  1. 5π/4 radians
  2. 91.7°
  3. 30°
  4.   2.44 radians

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