Question

Need help solving this trigonometry problem. We're solving for t (t means time) and the solution must be a positive number, which is where I am having problems.

I'll post the problem in equation form in a post below

Answer 1

\[-4\pi \sin(\pi t)=2\pi \cos(\pi t)\]

Answer 2

when I did this problem I get a negative number, which doesn't help because t is time, so it needs to be positive.

Answer 3

This is how I did it, I'll skip a couple steps to show you what I did. I divided -4pi from the left and cos(pi t) from the right and then got an equation like this

\[\tan(\pi t) = -1/2\]

Problem is when you do a reverse tangent, then divide by pi, I get -0.147583618 as my answer. But since the variable t is time, the answer can't be negative.

Answer 4

well tangent is negative in 2nd and 4th quadrants

most likely the calculator gave a negative angle (4th quadrant) when using inverse tangent

-- add pi to answer given from inverse tangent, this will give you the pos angle in 2nd quadrant

Answer 5

So does that mean I should add pi right after I do inverse tangent? And then after that divide pi on both sides to get t isolated. Or do you mean get t isolated and then add pi to the answer?

Answer 6

the former

t is time , (pi*t) is the angle

Answer 7

ok

Answer 8

Also for future reference, you can always convert a negative angle to a positive angle by simply adding 2pi

Answer 9

Alright I plugged in the answer I got back into the original equation and it's correct, so thanks very much for that tip. I'll remember that for the future.

Answer 10

yw