How do you graph #f(x)=sin (x/2 + pi/8)#?

1 Answer
Mar 8, 2018

Answer:

Graph it as you would normally graph #sin(x/2)#, but you need to shift the response to the left by #pi/4# radians, or 45 degrees.

Explanation:

Multiplying or dividing x in a sinusoidal function changes the frequency of the oscillation. Normally, #sin(x)# looks like this:
graph{sin(x) [-10, 10, -5, 5]}

If we plot #sin(x/2)#, it looks like this:
graph{sin(x/2) [-10,10,-5,5]}
See how it's half of the oscillations?

finally, I will plot #sin(x/2+pi/8)#, showing the leftward phase-shift
graph{sin(x/2+pi/8) [-10,10,-5,5]}

notice that the equation is 0 at x=#-pi/4#, which is that leftward shift.