Question

Trig...What would the equation of the function be if the graph of the function y = 2 sin (4x) is shifted left 45 degrees and down 2?

Answer 1

45 degrees = pi/4
by shifting left, this means the "starting" point is now x=-pi/4
4(-pi/4) +C = 0
--> C = pi

\[y = 2\sin(4x+\pi) -2\]

Answer 2

you can also show the shift this way:
4(x+pi/4) = 4x +pi