Question

can anyone help me find 't' when v=50 in the following equation please? (including steps)

v=100sin(200*pi*t+(pi/4))

Thanks in advance!

Answer 1

v=100sin(200*pi*t+(pi/4))

substitute 50 for v, giving us

50=100sin(200*pi*t+(pi/4))

divide both sides by 100, giving us

(1/2) = sin(200*pi*t+(pi/4))

with me so far?

Answer 2

@MathBiff

Answer 3

next step is to take the arcsin of both sides, which will "undo" the sin on the right side

arcsin(1/2) = 200*pi*t+(pi/4)

re-arrange to solve for t

Answer 4

cheers @Vocaloid. That's more or less where i got up to, the next step would be to subtract (pi/4) from both sides the divide both sides by 200*pi right?

(arcsin(1/2)-(pi/4))/200*pi=t

(30-(pi/4))/628.3=t

The other examples which I found on this question had 30+(pi/4). Just trying to find out which is right....

Here's the other example:

When V=50V
then 50V= 100Sin(200*pi*t+0.785)
50/100=Sin(200*pi*t+0.785)
(200*pi*t+0.785)=arcsin 50/100
=30degrees or 0.524rad

200*pi*t= 0.524+0.785 = 1.309

So when V=50v
Time t = 1.309/200*pi = 2.08ms

Answer 5

yeah, your answer looks right to me, I'm not sure how they got 30+(pi/4)

Answer 6

Ah cool. Thanks for that. I'm not exactly a math wizard so wasn't sure if I'd missed a trick somewhere. Have a good day!