Font (2 3) - + Letter spacing (4 5) - + Word spacing (6 7) - + Line spacing (8 9) - +

2.39 Appendix: Trigonometric functions

Generations of $A$ -level students have learned the basic trigonometric functions by means of SOHCAHTOA. In the usual right-angled triangle,

\sin x={{\hbox{opposite }}\over{\hbox{hypotenuse}}};\quad\cos x={{\hbox{% adjacent}}\over{\hbox{hypotenuse}}};\quad\tan x={{\hbox{opposite }}\over{\hbox% {adjacent}}}

Always use radians in calculations, and not degrees.

Identities which may be derived from the geometrical diagrams are:

\sin(-x)=-\sin x,\quad\cos(-x)=\cos x,\quad\sin\Bigl({{\pi}\over{2}}-x\Bigr)=% \cos x,

\cos\Bigl({{\pi}\over{2}}-x\Bigr)=\sin x,\quad\sin(\pi-x)=\sin x,\quad\cos(\pi% -x)=-\cos x.