# Math Help - y = sine x = cos x

1. ## y = sine x = cos x

If y = A*sin(Bx + C) + D is substituted as y = -1.5 sin(x + π/4) + 4, what

would the cosine function be in order to match the graph of said sine

function?

2. Originally Posted by zacharyrod
If y = A*sin(Bx + C) + D is substituted as y = -1.5 sin(x + π/4) + 4, what

would the cosine function be in order to match the graph of said sine

function?
Note that $\cos(x) = \sin \left(x - \frac{\pi}{2}\right)$. You can show this using the subtraction formula for sin. In terms of the graphs it means the graph of cos(x) is shifted by pi/2 to the right on the x axis

Only C would change as it's a phase difference

$-1.5\cos \left(x + \frac{\pi}{4} - \frac{\pi}{2}\right) + 4 = -1.5\cos \left(x - \frac{\pi}{4}\right) + 4$

3. -1.5cos(x-π/4)+4