For what value of c will y = sin1/2(x - c) be an even function? a. 2pi b. pi c. pi/2

c. pi/2

Step-by-step explanation:

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.

option b

Step-by-step explanation:

We are given that be an even function

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

We know that sin x is odd function and cos is even function

Odd function : when f(x) then the function is called an odd function.

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

Sin(-x)=-Sin x

Cos (-x)= Cos x

When we take C=

Then , y=Sin

y=

 ( )

When x is replace by -x

Then, we get

Hence, option a is false.

b.C=

When x is replaced by -x then we get

f(x)=f(-x) , Therefore, function is even,hence option b is true.

c.C=

When x is replaced by -x then we get

Hence, function is odd .Therefore, option c is false.

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step-by-step explanation:

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