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

Mar 8, 2018

Graph it as you would normally graph $\sin \left(\frac{x}{2}\right)$, but you need to shift the response to the left by $\frac{\pi}{4}$ radians, or 45 degrees.

#### Explanation:

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

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

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

notice that the equation is 0 at x=$- \frac{\pi}{4}$, which is that leftward shift.