# Latest Theory

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Content language: English

## Snippets

#### What are 'radians' ? One radian is the angle of an arc created by wrapping the radius of a circle ar

What are 'radians' ? One radian is the angle of an arc created by wrapping the radius of a circle around its circumference. In this diagram, the radius has been wrapped around the circumference to create an angle of 1 radian. The pink lines show the radius being moved from the inside of the circle to the outside: [nameofpicture.svg] The radius $$r$$ fits around the circumference of a circle exactly 2p times. That is why the circumference of a circle is given by: $$circumference = 2 \pi r$$

#### Converting radians to degrees: To convert radians to degrees, we make use of the fact that $$\pi$$

Converting radians to degrees: To convert radians to degrees, we make use of the fact that $$\pi$$ radians equals one half circle, or 180º. This means that if we divide radians by $$\pi$$, the answer is the number of half circles. Multiplying this by 180º will tell us the answer in degrees. So, to convert radians to degrees, multiply by $$\frac{180}{\pi}$$, like this: $$degrees = radians \times \frac{180}{\pi}$$

Converting degrees to radians: To convert degrees to radians, first find the number of half circles in the answer by dividing by 180º. But each half circle equals $$\pi$$ radians, so multiply the number of half circles by $$\pi$$. So, to convert degrees to radians, multiply by $$\frac{\pi}{180}$$, like this: $$radians = degrees \times \frac{\pi}{180}$$