Question

For the function y = 2 + 5 sin [ pi/12 (x-2)], what is the maximum value?

Answer 1

here is a normal sine wave ( hastily drawn :P )

Answer 2

This function that we have: \(\Large\rm y=5sin(Xstuff)+2\)

Answer 3

The stuff inside of the sine function just tells us about period and horizontal shifts, that won't affect our maximum at all. So we can ignore it.

Answer 4

The 5 is telling us the amplitude, how large the wave gets.

Answer 5

Normally sine gets up to 1,
Since we're multiplying by 5, it will get up to 5 at it's maximum.

But we have something else to deal with also!
See the +2? That's shifting our function vertically by 2.