## FANDOM

1,168 Pages

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

## Prerequisites

• Proof by definition of the functions: sine, cosine, and tangent as the ratios of their respective sides in a right triangle.
• $\sin \theta = \frac{\mathrm{opposite}}{\mathrm{hypotenuse}}$
• $\cos \theta = \frac{\mathrm{adjacent}}{\mathrm{hypotenuse}}$
• $\tan \theta = \frac{\mathrm{opposite}}{\mathrm{adjacent}}$

## Proof

Definition of Tangent:

$\tan \theta = \frac{\mathrm{opposite}}{\mathrm{adjacent}}$

$\tan \theta = \frac{\mathrm{opposite}}{\mathrm{adjacent}} \cdot 1$

$\tan \theta = \frac{\mathrm{opposite}}{\mathrm{adjacent}} \cdot \frac{\mathrm{hypotenuse}}{\mathrm{hypotenuse}}$

$\tan \theta = \frac{ \frac{\mathrm{opposite}}{\mathrm{hypotenuse}}}{\frac{ \mathrm{adjacent}}{\mathrm{hypotenuse}}}$

Definition of Sine and Cosine:

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

Community content is available under CC-BY-SA unless otherwise noted.