Trigonometric Ratios: sine, cosine and tangent

Given the right triangle $ABC$, we define the sine, the cosine and the tangent of an angle $x$ as:

1. $\sin (x)$: the sine of the angle $x$ is the ratio between the opposite cathetus and the hypotenuse: $$\sin (x)={\displaystyle \frac{a}{c}}$$

2. $\cos (x)$: the cosine is the ratio between the adjoining cathetus and the hypotenuse: $$\cos (x)={\displaystyle \frac{b}{c}}$$

3. $\tan (x)$: the tangent is defined as the ratio between the opposite cathetus and the adjoining one: $$\tan (x)={\displaystyle \frac{a}{b}}$$