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Radian

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Algebra and Trigonometry

Definition

A radian is a unit of angular measure where the angle subtended at the center of a circle by an arc whose length is equal to the circle's radius. One full revolution around a circle is $2\pi$ radians.

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5 Must Know Facts For Your Next Test

  1. There are $2\pi$ radians in a full circle, equivalent to 360 degrees.
  2. To convert degrees to radians, multiply by $\frac{\pi}{180}$.
  3. To convert radians to degrees, multiply by $\frac{180}{\pi}$.
  4. An angle of $\pi$ radians corresponds to 180 degrees.
  5. The unit circle uses radians to define angles for sine and cosine functions.

Review Questions

  • How many radians are there in a full circle?
  • Convert an angle of 90 degrees to radians.
  • What is the radian measure for an angle that corresponds to one-quarter of a circle?
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