Question

Read the section and make your own summary of the material.

Short answer

The trigonometry identities use to find the sides and angle of the triangle.

Step-by-step solution

Introduction

In this section learn about trigonometry and the Pythagorean theorem. It is applicable in a right-angle triangle. There are two sides and one hypotenuse. The hypotenuse is the longest side of the triangle.

Explanation

In triangle $ABC$ , $\mathrm{\angle }B={90}^{\circ }$

There are trigonometry identities:

$\begin{array}{rlr}\bullet & & {\sin }^{2}C+{\cos }^{2}C=1\\ \bullet & & {\sec }^{2}C=1+{\tan }^{2}C\\ \bullet & & {\csc }^{2}C=1+{\cot }^{2}C\end{array}$

$\sin C=\frac{c}{b}$

$\cos C=\frac{a}{b}$

$\tan C=\frac{c}{a}$

Using this identity relation between $\sin C,\cos C$ and $\tan C$.

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