# How do you graph y = sin(pi/2x + (3pi)/2)?

Jan 8, 2018

I'm assuming you want

$y = \sin \left(\frac{\pi}{2} x + \frac{3 \pi}{2}\right)$

In standard form. Use the sum formula for sine, which is $\sin \left(A + B\right) = \sin A \cos B + \cos A \sin B$.

$y = \sin \left(\frac{\pi}{2} x\right) \cos \left(\left(3 \frac{\pi}{2}\right)\right) + \cos \left(\frac{\pi}{2} x\right) \sin \left(\frac{3 \pi}{2}\right)$

As long as you know you trigonometric function values at $\frac{\pi}{2}$ and $\frac{3 \pi}{2}$, you're good to go.

$y = \sin \left(\frac{\pi}{2} x\right) \left(0\right) - 1 \left(\cos \left(\frac{\pi}{2} x\right)\right)$

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

If you graph $f \left(x\right) = \sin \left(\frac{\pi}{2} x + \frac{3 \pi}{2}\right)$ and $g \left(x\right) = - \cos \left(\frac{\pi}{2} x\right)$, you'll see they're indeed the same graphs.

Hopefully this helps!