For what value of C will y = sin (x - C) be an even function?

a. 2π

b. π

c. π/2

The answer is the option c. pi/2.

You must know that y = sin (x) is an odd function and also that y = cos (x) is an even function.

Also, you should know that sin (x + pi/2) = cos (x).

You can show it using the definition of the functions sine and cosine in the unit circle or using the formula of the sine of a sum: sin (A + B) = sin (A) * cos (B) + cos (A) * sin (B).

When you substitute B with pi/2 you get sin (A + pi/2) = sin (A) * 0 + cos (A) * 1 = cos (A).

Then, given that cos (A) is even sin (A+pi/2) is even.