What is the period of the function f(x)=sin(x pi/6 + pi/4)?

Question

What is the period of the function f(x)=sin(x pi/6 + pi/4)?

Answer 1

The standard way of writing a sine function to identify its components is:

f(x) = a•sin [b(x-c)] + d

Where:

|a| = amplitude

2π / b = period

c = phase shift (horizontal shift)

d = vertical shift

Given:

f(x) = sin(πx/6 + π/4)

First thing is factor out π/6 inside the sine function to see it clearly.

f(x) = sin [(π/6)(x + 3/2)]

That means:

amplitude = |a| = 1

period = 2π / (π/6) = 12

c = 3/2

d = 0