Maths trig notes:

Created by: Catchupman
Created on: 28-09-17 15:07

Trigonometry:

Radians:

Angles can be measured in either radians or degrees where $180^\circ = \pi (http://www.bbc.co.uk/staticarchive/fcd601e6443807f52f970bf5e5f0dc69385d811f.gif)$ radians. If you know that $180^\circ = \pi (http://www.bbc.co.uk/staticarchive/fcd601e6443807f52f970bf5e5f0dc69385d811f.gif)$ radians, you can easily convert between the two.

To convert from degrees to radians, $a^ \circ \to {a \over {180}} \times \pi \; rads (http://www.bbc.co.uk/staticarchive/e144ccbc9872a0ed5dda5469c785cb1fbb1e32f2.gif)$

So 30° converts to radians as follows:

${{30} \over {180}}\;\pi (http://www.bbc.co.uk/staticarchive/f7d0709ca62d1abbca19ae942902bbfb15345eef.gif)$ = ${\pi \over 6} (http://www.bbc.co.uk/staticarchive/30eb8d209eba01619ba4a87e2e7c14dacc8c0f7f.gif)$ or ${1 \over 6}\pi (http://www.bbc.co.uk/staticarchive/bfd3edc9aa2bdbded771e30220188e94759ef8be.gif)$ radians

To convert from radians to degrees, $\theta \; rads \to {\theta \over \pi } \times 180^\circ (http://www.bbc.co.uk/staticarchive/97ef9112b4e54a0f0f6cbd1664697526f19a9825.gif)$ . If the angle contains $\pi (http://www.bbc.co.uk/staticarchive/ae4811472b284dedd6898069acb15201c279bb20.gif)$ , simply replace $\pi (http://www.bbc.co.uk/staticarchive/ae4811472b284dedd6898069acb15201c279bb20.gif)$ with 180° as shown below.

To convert ${\pi \over 4} (http://www.bbc.co.uk/staticarchive/c6b089d05d96941887d4f583e89197082b90d7f1.gif)$ radians into degrees

${{180^ \circ } \over 4} (http://www.bbc.co.uk/staticarchive/c1ba6e59b8e40e1d711c2591fba22bd1b70eeb48.gif)$ = $45^ \circ (http://www.bbc.co.uk/staticarchive/6c9f170fc1e9b8d269cabd1bdfb76c2d978efc48.gif)$