# How can I rearrange this for the angle?

## Main Question or Discussion Point

also - The result I'm getting for d is 18587 - this is when I enter 427 for initial velocity, 45 for theta, and 9.81 for g - is this correct?

To rearrange, use inverse operations to move things you don't want to the other side -

You're dividing the RHS by g, so multiply both sides by g
You're multiplying the RHS by v^2 so divide both sides by v^2
Then use the inverse sin function
etc.

To see if it's correct, compare the result to some other method for estimating the same thing, or even just your intuition.

HallsofIvy
Homework Helper
I get 18586- with decimal part .o345...

To solve for $\theta$, "unpeel" what has been done:
$$d= \frac{v^2sin(2\theta)}{g}$$
so, multiplying both sides by g,
$$dg= v^2 sin(2\theta)[/itex] dividing both sides by $v^2$, [tex]\frac{dg}{v^2}= sin(2\theta)$$
Taking the inverse sine (arcsin) of both sides
(be careful- since sine is not one-to-one there is no "true" inverse- there are an infinite number of angles with the same sine- two between 0 and pi/2- and "arcsin" only gives one of them)
$$arcsin\left(\frac{dg}{v^2}\right)= 2\theta$$
and, finally, divide both sides by 2:
$$\frac{1}{2}arcsin\left(\frac{dg}{v^2}\right)= \theta$$

Thanks guys - that was a massive help.