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!!!!
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).`
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))`