Chapter 7.2, Problem 3CFU

To determine

To explain: the reason for the given statement.

Answer to Problem 3CFU

The other trigonometric functions are easier to solve in simpler forms when they are written in terms of sine and cosine.

Explanation of Solution

Given information:

In trigonometric identity both sides are often rewritten in terms of sine and cosine.

Calculation:

The trigonometric functions $\csc x$ , $\sec x$ , $\tan x$ and $\cot x$ can be written in simpler form as follows:

  $\begin{array}{l}\csc x=\frac{1}{\sin x}\left[\text{Reciprocal identity}\right]\\ \sec x=\frac{1}{\cos x}\left[\text{Reciprocal identity}\right]\\ \tan x=\frac{\sin x}{\cos x}\left[\text{Quotient identity}\right]\\ \cot x=\frac{\cos x}{\sin x}\left[\text{Quotient identity}\right]\end{array}$

Since the trigonometric functions (except sine and cosine) can be written in simpler forms as shown above that are much easier to solve. Thus both sides in trigonometric identity are often rewritten in terms of sine and cosine.