1. ## Sketching Sine Graphs

Hi there!
How would you sketch this graph?

y=2sin(x-pi/2)+1
Any help much appreciated!
Your function is $f(x)=2\sin(x-\tfrac{\pi}{2})+1$.
The general sine function is $f(t)=A\sin(Bt-C)+D$.
For the general sine function, |A| is the amplitude, B is the period, and D is the vertical shift. You then use $\frac{C}{B}$ to find the phase shift.
Your phase shift is $\frac{C}{B}=\frac{\pi/2}{1}=\pi/2$. This means that your phase shift is to the right by $\tfrac{\pi}{2}$.