1. ## Sketching Sine Graphs

Hi there!
How would you sketch this graph?

y=2sin(x-pi/2)+1
Any help much appreciated!

2. ## Re: Sketching Sine Graphs

Your function is $\displaystyle f(x)=2\sin(x-\tfrac{\pi}{2})+1$.

The general sine function is $\displaystyle f(t)=A\sin(Bt-C)+D$.

For the general sine function, |A| is the amplitude, B is the period, and D is the vertical shift. You then use $\displaystyle \frac{C}{B}$ to find the phase shift.

Your function has an amplitude of 2, a period of 1, and a vertical shift of 1. Note that since D is positive, your shift will be 1 unit upward from the x-axis.

Your phase shift is $\displaystyle \frac{C}{B}=\frac{\pi/2}{1}=\pi/2$. This means that your phase shift is to the right by $\displaystyle \tfrac{\pi}{2}$.