# Thread: Help with a trig question - Solving for variable

1. ## Help with a trig question - Solving for variable

Hello everyone, just having some trouble with my assignment.

I had to find the equation for velocity using the equation for vertical displacement so I did. The question asks to find the vertical displacement when the velocity is 0.8 m/s so as you can see I subbed it into the equation above. Problem is, im having trouble solving for 't'.

Can anyone help?... It would be much appreciated.

Ill need a lot of help for calculus so I hope I don't bother these forums!

2. $\displaystyle 0.8= -1.2sin(2t)+0.8cos(t)$

Use double angle formula

$\displaystyle 0.8= -1.2sin(t)cos(t)+0.8cos(t)$

Factor out cos(t)

$\displaystyle 0.8= cos(t)(0.8-1.2sin(t))$

can you solve it from here?

3. Originally Posted by pickslides
$\displaystyle 0.8= -1.2sin(2t)+0.8cos(t)$

Use double angle formula

$\displaystyle 0.8= -1.2{\color{red}(2)}sin(t)cos(t)+0.8cos(t)$
$\displaystyle 0.8= {\color{red}-2.4}sin(t)cos(t)+0.8cos(t)$

Factor out cos(t)

$\displaystyle 0.8= cos(t)(0.8-{\color{red}2.4}sin(t))$

can you solve it from here?
Quoted with minor corrections.

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4. Originally Posted by DrCheeky

Hello everyone, just having some trouble with my assignment.

I had to find the equation for velocity using the equation for vertical displacement so I did. The question asks to find the vertical displacement when the velocity is 0.8 m/s so as you can see I subbed it into the equation above. Problem is, im having trouble solving for 't'.

Can anyone help?... It would be much appreciated.

Ill need a lot of help for calculus so I hope I don't bother these forums!

Originally Posted by pickslides
$\displaystyle 0.8= -1.2sin(2t)+0.8cos(t)$

Use double angle formula

$\displaystyle 0.8= -1.2sin(t)cos(t)+0.8cos(t)$

Factor out cos(t)

$\displaystyle 0.8= cos(t)(0.8-1.2sin(t))$

can you solve it from here?
I don't see how this (or its corrected incarnation) helps get an exact solution. It's 0.8 on the left hand side, not 0 ....

5. $\displaystyle 0.8 = -1.2sin2t + 0.8cost$

$\displaystyle 1 = -1.5sin2t + cost$(Divided everything by 0.8)

$\displaystyle 1 = -1.5(2)sintcost + cost$ (Provided by you guys, correct?)

$\displaystyle 1 = -3sintcost + cost$

$\displaystyle 1 = cost (-3sint + 1)$(Factored out cost)

$\displaystyle 0 = -3sint + 1$(cos^-1 on the other side)

$\displaystyle -1 = -3sint$

$\displaystyle t = sin^-1(-1/-3)$

$\displaystyle t = 0.34$

Can anyone see if thats correct?

6. Originally Posted by DrCheeky
$\displaystyle 0.8 = -1.2sin2t + 0.8cost$

$\displaystyle 1 = -1.5sin2t + cost$(Divided everything by 0.8)

$\displaystyle 1 = -1.5(2)sintcost + cost$ (Provided by you guys, correct?)

$\displaystyle 1 = -3sintcost + cost$

$\displaystyle 1 = cost (-3sint + 1)$(Factored out cost)

$\displaystyle 0 = -3sint + 1$(cos^-1 on the other side) No, you cannot do that!

$\displaystyle -1 = -3sint$

$\displaystyle t = sin^-1(-1/-3)$

$\displaystyle t = 0.34$

Can anyone see if thats correct?
No, not correct. See the red in the quote.

$\displaystyle \cos^{-1}(\cos t) = t$ (assuming that we are mindful of the domain and range), but $\displaystyle \cos^{-1}[\cos t (-3\sin t + 1)] \neq -3\sin t + 1$.

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7. So what else can I do?

I'm 100% I got up to this part right so far (finding the derivative of vertical displacement equation and subbing in velocity). Cant find this t value!

8. Originally Posted by DrCheeky
So what else can I do?

I'm 100% I got up to this part right so far (finding the derivative of vertical displacement equation and subbing in velocity). Cant find this t value!

9. DrCheeky, you mentioned finding the derivative of the vertical displacement equation. What is it, out of curiosity?

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10. Originally Posted by mr fantastic

Mr. Fantastic asked a question. Answer it PLEASE. I'm dying to see the resolution to this problem.

I have a question of my own. Is that the displacement function, or the velocity function? Because if you set the displacement function = 0.8, you made a boo boo.

Find the velocity function by taking the derivative of the displacement function. Set THAT equal to 0.8, solve for t, and then plug that value of t into the displacement funtion. This is what you must do.

Or if you were given the velocity function, find the displacement funtion by integrating the velocity function. Or were you given both functions?

Please post the question so as to eliminate any further confusion.