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Class Summary for Thursday May 31, 2007

Aim: What are Radians?

A Radian is the length of an arc measured out by an angle on the unit circle. Basically, a Radian is another way of calculating the length of an arc without expressing the final result in degree form. This is important because it is much easier to express answers in numbers. Radians usually contain pi in the answer and should we need to convey mathematical methods and answers to a different life form we would be able to use radians instead of degrees.

Some Important Radians to Remember for Grade 11 and the Future are:

$30^{\circ} = (\frac{30}{360}) \times\2\pi\ = \frac{\pi}{6}$
$45^{\circ} = (\45\div\ 360) \times\2\pi\ = \pi\div\4$
$60^{\circ} = (\60\div\ 360) \times\2\pi\ = \pi\div\3$
$90^{\circ} = (\90\div\ 360) \times\2\pi\ = \pi\div\2$
$180^{\circ} = (\180\div\ 360) \times\2\pi\ = \pi\$
$360^{\circ} = (\360\div\ 360) \times\2\pi\ = 2\pi\$

The left side of the equation is in degrees mode, the middle of the equations is the conversion from degrees to radians and the result, on the right side of the equation is the same number of degrees in Radian mode. the above cases are for when the radius of the unit circle is 1, which it always is. The generic formula for the conversion from degrees to radians is:

$Degrees = Angle \times\2\pi\ radius = Radian$

Radians are just a different form of calculating the lengths of arcs using the Unit Circle.

Thanks,
Matein

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Class Summary for Thursday May 31, 2007

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