Inverse trigonometric ratios: cosecant, secant and cotangent

In this section, we are going to define the inverse trigonometric ratios, this is, the inverse ratios of the sine, the cosine and the tangent. Given a triangle rectangle, we define the cosecant, the secant and the cotangent of an angle $x$ as the inverse ratios of the sine, the cosine and the tangent, respectively.

• $\csc (x)$: the cosecant is the inverse of the sine or, also, its multiplicative inverse: $$\csc (x)={\displaystyle \frac{1}{\sin (x)}}={\displaystyle \frac{c}{a}}$$

• $\sec (x)$: the secant is the inverse of the cosine or, also, its multiplicative inverse: $$\sec (x)={\displaystyle \frac{1}{\cos (x)}}={\displaystyle \frac{c}{b}}$$

• $\cot (x)$: the cotangent is the inverse of the tangent or, also, its multiplicative inverse: $$\cot (x)={\displaystyle \frac{1}{\tan (x)}}={\displaystyle \frac{b}{a}}$$