Mathematics, 25.06.2019 21:00 hihowareyou12

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

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Answer from: quadyshia12370

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.

Answer from: cody4976

option b

Step-by-step explanation:

We are given that $y=sin \frac{1}{2}(x-C)$ 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) $\neqf(-x)$ 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= $2\pi$

Then , y=Sin $\frac{x}{2}-\frac{2\pi}{2}$

y= $sin(\frac{x}{2}-\pi)$

$y=-sin\frac{x}{2}$ ( $sin (x-\pi)=-sin x$ )

When x is replace by -x

Then, we get $y=-sin(-\frac{x}{2})=sin\frac{x}{2}$

$f(-x)\neq f( x)$

Hence, option a is false.

b.C= $\pi$

$y= sin (\frac{x}{2}-\frac{\pi}{2})$

$y=-sin(\frac{\pi}{2}-\frac{x}{2})$

$y=-cos \frac{x}{2}$

When x is replaced by -x then we get

$y=-cos (-\frac{x}{2})=- cos \frac{x}{2}$

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

c.C= $\frac{\pi}{2}$

$y=sin (\frac{x}{2}-\frac{\pi}{4})$

Sin (A-B)=Sin A Cos B- Sin B Cos A

$[y= sin \frac{x}{2} cos {\frac{\pi}{4}-cos\frac{x}{2} sin\frac{\pi}{4}$

$sin\frac{\pi}{4}= cos \frac{\pi}{4}=\frac{1}{\sqrt2}$

$y=\frac{1}{\sqrt2}(sin \frac{x}{2}- cos \frac{x}{2})$

When x is replaced by -x then we get

$y=\frac{1}{\sqrt2}(-sin\frac{x}{2}-cos \frac{x}{2})$

$f(x)\neq f(-x)$

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

Answer from: Quest

Letter a i would say
In the diagram below, ab is parallel to cd. what is the value y? a.150b.50c.60d.30

Answer from: Quest

required rate of return = 0.166 = 16.6%

step-by-step explanation:

under the capital asset pricing model (capm), the required or expected rate of return for a particular security or asset is given using the formula:

required rate of return = risk-free rate + beta*(market risk premium)

we are given that;

risk-free rate = 4% = 0.04

beta = 1.4

market risk premium = 9% = 0.09

we simply plug these values into the above formula;

required rate of return = 0.04 + 1.4*(0.09)

required rate of return = 0.04 + 0.126

required rate of return = 0.166 = 16.6%

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