Hi there!
How would you sketch this graph?
y=2sin(x-pi/2)+1
Any help much appreciated!
Thank you in advance
~Ebony Jade :-)
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 $\displaystyle \tfrac{\pi}{2}$.