Angles

Angles

The main things to remember about angles is that they are measured starting from the positive x-axis, unless otherwise stated, and measured in a counter-clockwise direction.

We say that a whole revolution is 360 degrees, making an arrow pointing north a 90 degree angle, west a 180 angle, and south a 270 degree angle.

Radians

If we have an angle in degrees and we want the angle measure in radians we can use the conversion facto of $180^{\circ }=\pi {\text{ radians}}$ This means that if we want to convert back and forth $1{\text{ degree}}={\frac {\pi }{180}}{\text{ radians}}\qquad 1{\text{ radian }}={\frac {180}{\pi }}{\text{ degrees}}$

Examples

Convert the following from degrees to radians or radians to degrees

$1.\,245^{\circ }$

$2.\,{\dfrac {5\pi }{4}}$

$3.\,275^{\circ }$

$4.\,{\dfrac {9\pi }{2}}$

$5.\,30^{\circ }$

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