SL 3.2—2d and 3d trig

Trigonometric ratios relate the angles of a right-angled triangle to the ratios of its sides. Before applying any ratio, you must label the triangle's sides relative to the angle you're working with, usually called $\theta$.

The three sides are:

• Hypotenuse — the longest side, always opposite the right angle
• Opposite — the side that does not touch the angle $\theta$
• Adjacent — the non-hypotenuse side that does touch the angle $\theta$

The three primary trigonometric ratios are:

$\sin \theta =\frac{\text{opposite}}{\text{hypotenuse}},\cos \theta =\frac{\text{adjacent}}{\text{hypotenuse}},\tan \theta =\frac{\text{opposite}}{\text{adjacent}}$

There is also an important relationship between $\tan \theta$, $\sin \theta$, and $\cos \theta$. Dividing $\sin \theta$ by $\cos \theta$:

$\frac{\sin \theta }{\cos \theta }=\frac{\frac{\text{opposite}}{\text{hypotenuse}}}{\frac{\text{adjacent}}{\text{hypotenuse}}}=\frac{\text{opposite}}{\text{adjacent}}=\tan \theta$

So: $\tan \theta =\frac{\sin \theta }{\cos \theta }$