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Maths

Radians and equations

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Radians and degrees

Angles can be measured in either radians or degrees where 180^\circ = \pi radians. If you know that 180^\circ = \pi radians, you can easily convert between the two.

To convert from degrees to radians, a^ \circ \to {a \over {180}} \times \pi \; rads

So 30° converts to radians as follows:

{{30} \over {180}}\;\pi = {\pi \over 6} or {1 \over 6}\pi radians

Convert 125° into radians.

{{125} \over {180}}\;\pi = {{25} \over {36}}\;\pi or {{25\pi } \over {36}} radians

To convert from radians to degrees, \theta \; rads \to {\theta \over \pi } \times 180^\circ. If the angle contains \pi, simply replace \pi with 180° as shown below.

To convert {\pi \over 4} radians into degrees

{{180^ \circ } \over 4} = 45^ \circ

Convert a value of 2 radians into degrees.

2\;rads = {2 \over \pi } \times 180^ \circ = 114.6^ \circ (to 1 decimal place)

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SQA - Maths

Scottish Qualifications Authority Maths resources, including Past Papers, Arrangements Documents, and Marking Guidelines.

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