Trigonometry

In a right angled triangle, the side opposite the right angle is called the hypotenuse.

If one of the other angles is x^\circ, then we can label the remaining sides as shown in this diagram.

Triangle x∞ angle. The sides labelled as Hypotenuse, Opposite (to x∞) and Adjacent (to x∞)

There are 3 trig ratios you need to know:

  • sine
  • cosine
  • tangent

We shorten these to:

  • sin
  • cos
  • tan

The three important ratios are:

\sin (x^\circ ) = \frac{{opposite}}{{hypotenuse}}

\cos (x^\circ ) = \frac{{adjacent}}{{hypotenuse}}

\tan (x^\circ ) = \frac{{opposite}}{{adjacent}}

Triangle x° angle. The sides labelled as Hypotenuse, Opposite and Adjacent

Some people remember a well-known mnemonic using the first letters to help when deciding which ratio to use for each trig problem.

This mnemonic is:

SOH CAH TOA

These letters stand for:

S sine O opposite H hypotenuse

C cosine A adjacent H hypotenuse

T tangent O opposite A adjacent