Question

Which function is the same as y=3cos(2(x+pi/2))-2?

Answer 1

Answer:

Option B is Correct.

Step-by-step explanation:

Given: $y\,=\,3\,cos\,(2(x+\frac{\pi}{2}))-2$

To find: Equivalent Expression.

We use Following functions:

$cos\,(\pi+x)=\,-cos\,x\:,\:cos\,(\frac{\pi}{2}+x)=\,-sin\,x\:\:and\:\:sin\,(\frac{\pi}{2}+x)=cos\,x$

First we simply the given expression,

$y\,=\,3\,cos\,(2(x+\frac{\pi}{2}))-2$

$y\,=\,3\,cos\,(2x+2\frac{\pi}{2}))-2$

$y\,=\,3\,cos\,(2x+\pi)-2$

$y\,=\,3\,cos\,(\pi+2x)-2$

$y\,=\,3\,(-cos\,2x)-2$     ( using above mentioned result )

$y\,=\,-3\,cos\,2x-2$ ............................(1)

Option A:

$y\,=\,3\,sin\,(2(x+\frac{\pi}{4}))-2$

$y\,=\,3\,sin\,(2x+2\frac{\pi}{4}))-2$

$y\,=\,3\,sin\,(2x+\frac{\pi}{2})-2$

$y\,=\,3\,sin\,(\frac{\pi}{2}+2x)-2$

$y\,=\,3\,cos\,2x-2$     ( using above mentioned result )

Since, it is not equal to (1)

Therefore, It is Not correct Option.

Option B:

$y\,=\,-3\,sin\,(2(x+\frac{\pi}{4}))-2$

$y\,=\,-3\,sin\,(2x+2\frac{\pi}{4}))-2$

$y\,=\,-3\,sin\,(2x+\frac{\pi}{2})-2$

$y\,=\,-3\,sin\,(\frac{\pi}{2}+2x)-2$

$y\,=\,-3\,cos\,2x-2$     ( using above mentioned result )

Since, it is equal to (1)

Therefore, It is Correct Option.

Option C:

$y\,=\,3\,cos\,(2(x+\frac{\pi}{4}))-2$

$y\,=\,3\,cos\,(2x+2\frac{\pi}{4}))-2$

$y\,=\,3\,cos\,(2x+\frac{\pi}{2})-2$

$y\,=\,3\,cos\,(\frac{\pi}{2}+2x)-2$

$y\,=\,3\,(-sin\,2x)-2$     ( using above mentioned result )

$y\,=\,-3\,sin\,2x-2$

Since, it is not equal to (1)

Therefore, It is Not correct Option.

Option D:

$y\,=\,-3\,cos\,(2(x+\frac{\pi}{2}))-2$

$y\,=\,-3\,cos\,(2x+2\frac{\pi}{2}))-2$

$y\,=\,-3\,cos\,(2x+\pi)-2$

$y\,=\,-3\,cos\,(\pi+2x)-2$

$y\,=\,-3\,(-cos\,2x)-2$    ( using above mentioned result )

$y\,=\,3\,cos\,2x-2$

Since, it is not equal to (1)

Therefore, It is Not correct Option.

Therefore, Option B is Correct.

Answer 2

The Answer is B i just took the test on ingenuity.