what is the period?

Question

What is the period? fractions confuse me

2 sin 4(x+pi/4)

Answer 1

This is 2sin(4x+pi)
The 2 and pi have nothing to do with the period.
The wavelength or period is 2pi/4 = pi/2

In general, the graph of y = a sin(bx+c) is a simple waveform curve with amplitude = a, wavelength= period = 2pi/b, and differing in phase from that of y=sin x by -c/b.

Answer 2

Remember, for y=asin(k(x + theta))+d,

period = 360/k

in this case, it would be pi/2