Question

Write another possible formula for
y = −2 cos(3x + π) + 1 using the sine
function and a positive coefficient on the sine.

Answer 1

remember
\[\cos(x)=\sin(\frac{\pi}{2}-x)\]
\[y=-2\sin(\frac{\pi}{2}-(3x+\pi))+1\]

Answer 2

you can simplify that inside

Answer 3

wait, so you have t plug it in? so how would you handle the pi in the original equation? ugh I'm really bad at all these identities.

Answer 4

you have
\[y=-2\sin(\frac{\pi}{2}-3x-\pi)+1=-2\sin(\frac{\pi}{2}-\frac{2\pi}{2}-3x)+1\]
\[y=-2\sin(\frac{-\pi}{2}-3x)+1\]
and it also say to write with positive coeifficient
so also recall that sin(-x)=-sinx
so we have
\[y=-2\sin(-[\frac{\pi}{2}+3x])+1=-2*-\sin(\frac{\pi}{2}+3x)+1=2\sin(\frac{\pi}{2}+3x)+1\]