Explain how to transform: y=2sin(2x-pi) to y=2sin2(x-pi/2) All I see is factoring out by 2, but I dont think that the answer!! Please I need an explanation!!!!

Expert Answers

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You need to bring the terms into the difference `x-pi/2`  to a common denominator such that:

`x-pi/2 = (2x-pi)/2`

You need to write the function again such that:

`y = 2sin2*(x-pi/2) => y = 2sin2*((2x-pi)/2)`

Reducing by 2 yields:

`y = 2sin(2x-pi)`

Hence, performing the factorization to the function `y = 2sin2*(x-pi/2)`  yields that its equivalent form is exactly the function provided by the problem, `y=2sin(2x-pi).`

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The sine of an angle X is the same as the sine of twice the angle X divided by 2. `X = 2*(X/2)`

Using this, `y = 2sin(2x-pi)` is transformed to `y=2sin2(x-pi/2) ` merely by factoring out 2 from the brackets. The process does not require anything else to be done.

y = `2sin(2x-pi)`

=> `y = 2sin(2*x-2*pi/2)`

=> `y = 2sin(2*(x-pi/2))`

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