Chapter 1, Problem 24RE

To determine

To check: Whether the function $y=1-\sin x$ is even, odd or neither.

Answer to Problem 24RE

The function $y=1-\sin x$ is neither even nor odd.

Explanation of Solution

Given information: The given function is $y=1-\sin x$ .

Calculation:

Even function: A function $f\left(x\right)$ is said to be an even function if it satisfies the condition $f\left(-x\right)=f\left(x\right)$ .

Odd function: A function $f\left(x\right)$ is said to be an odd function if it satisfies the condition $f\left(-x\right)=-f\left(x\right)$ .

Substitute $-x$ for $x$ in the given function $y=f\left(x\right)=1-\sin x$ .

  $\begin{array}{c}f\left(-x\right)=1-\sin \left(-x\right)\\ =1+\sin x\\ \ne f\left(x\right)\\ \ne -f\left(x\right)\end{array}$

Therefore, the function $y=1-\sin x$ is neither even nor odd.