For what value of C will y = sin(x - C) be an even function? a. 2π b. π c. π/2

Question

asked Oct 1, 2018 197k views

2 Answers

M Somerville · Answer 1 · 2018-10-05T21:38:00+0000

Answer:

c.
$(\pi)/(2)$

Explanation:

We are given that

y=sin(x-C)

We have to find the value of C for which given function is even function.

We know that

Even function : If f(x)=f(-x) then the function is called even function.

$a.2\pi$

Substitute the value then we get

$y= sin(x-2\pi)= sin(-(2\pi-x))=-sin (2\pi-x)=sin x$

We know that sin (-x)=-sin x,
$sin(2\pi-x)=-sinx$

We know that Sin x is an odd function , therefore, option a is incorrect.

b.
$\pi$

Substitute the value then we get

$y= sin (x-\pi)=sin(-(\pi-x))=-sin (\pi-x)=-sin x$

It is an odd function.

Hence, option b is incorrect.

c.
$(\pi)/(2)$

Substitute the value then we get

$y= sin(x-(\pi)/(2))=sin(-((\pi)/(2)-x))=-sin((\pi)/(2)-x)=-cos x$

$sin((\pi)/(2)-x)=cosx$

We know that cos x is even function

Replace x by -x then, we get

-cos (-x)=-cos x ....(cos (-x)=cos x)

Hence, the value of C=
$(\pi)/(2)$ for which given function will be an even function.

Answer:c.
$(\pi)/(2)$