How do you graph y = 2sin(theta+90°)?

May 15, 2018

See below.

Explanation:

First of all, observe that $\sin \left(\setminus \theta + \frac{\pi}{2}\right) = \cos \left(\setminus \theta\right)$. So, your equation becomes

$y = 2 \cos \left(\setminus \theta\right)$.

From here, assuming you're familiar with the graph of the "standard" cosine function $y = \cos \left(\setminus \theta\right)$, you only have a vertical stretch: every transformation of the form $f \left(x\right) \setminus \mapsto k f \left(x\right)$ results in a vertical stretch if $| k | > 1$, or a vertical compression otherwise. In your case, the graph is stretched by a factor of two, meaning that the amplitude of the cosine waves will range between $- 2$ and $2$, instead of the usual $\left[- 1 , 1\right]$ interval.

Here you can see the two function graphed together: you can see how the run "at the same speed" horizontally, meaning that the zeroes, maxima and minima are vertically aligned, but also that one of the functions oscillates with wider range.