Basic Trigonometric ratios using a right triangle

For a right triangle with one acute angle $\theta$, label the side opposite $\theta$, the side adjacent to $\theta$, and the hypotenuse. Six ratios can be formed from these three lengths, and each is given its own name and defines one of the six basic trigonometric functions.

The two "primary" ratios are

The remaining four are all built from $\sin\theta$ and $\cos\theta$:

$\tan\theta = \frac{\sin\theta}{\cos\theta}, \qquad \cot\theta = \frac{\cos\theta}{\sin\theta}, \qquad \sec\theta = \frac{1}{\cos\theta}, \qquad \csc\theta = \frac{1}{\sin\theta}.$ …