# Thread: Need help solving sinusoidal functions

1. ## Need help solving sinusoidal functions

I am having trouble solving the the "x" value of a sinusoidal function when given the y value.

Here is a sample question:

d(t) = 2 sin(30t) + 5, solve for t when given the d value of 3 m.

Also another question, T(t) = - 18.9cos30t + 5.8 solve for t when given the T value of 2.

2. Originally Posted by oceanblack
I am having trouble solving the the "x" value of a sinusoidal function when given the y value.

Here is a sample question:

d(t) = 2 sin(30t) + 5, solve for t when given the d value of 3 m.

Also another question, T(t) = - 18.9cos30t + 5.8 solve for t when given the T value of 38.

If d=3, then the first equation becomes $3=2\sin\!\left(30t\right)+5\implies 2\sin\!\left(30t\right)=-2\implies \sin\!\left(30t\right)=-1$.

To make it a little easier, let $\omega=30t$ so $\sin \omega=-1$. Now what values of $\omega$ cause this to be true? Take those value(s) and divide them by 30 to find t.

Can you try to do something similar for the second problem?

3. Originally Posted by Chris L T521
If d=3, then the first equation becomes $3=2\sin\!\left(30t\right)+5\implies 2\sin\!\left(30t\right)=-2\implies \sin\!\left(30t\right)=-1$.

To make it a little easier, let $\omega=30t$ so $\sin \omega=-1$. Now what values of $\omega$ cause this to be true? Take those value(s) and divide them by 30 to find t.

Can you try to do something similar for the second problem?
I'm unsure as to how to find what values cause this to be true.

I tried to do the inverse of sine and I got -90, but dividing that by 30 got me the answer of -3 which is not the given answers of 60, 180 and 300.

May you please give more detail as to how I find the appropriate values for w, is it guessing and checking? I am unsure.

Thank you for helping me so far, I greatly appreciate it.

4. Originally Posted by oceanblack
I am having trouble solving the the "x" value of a sinusoidal function when given the y value.

Here is a sample question:

d(t) = 2 sin(30t) + 5, solve for t when given the d value of 3 m.
$d(t) = 2 \sin(30t) + 5$

$3 = 2 \sin(30t) + 5$

$-2 = 2 \sin(30t)$

$-1 = \sin(30t)$

$30t = \sin^{-1} (-1) = \frac{3\pi}{2} + 2k\pi$, $k = 0,1,2, \cdots$

solve for $t$.

Also another question, T(t) = - 18.9cos30t + 5.8 solve for t when given the T value of 38.
the max value of $T = 18.9 + 5.8 = 24.7$ so there is no $t$ satisfy $T(t) = 38$

5. Originally Posted by dedust
$d(t) = 2 \sin(30t) + 5$

$3 = 2 \sin(30t) + 5$

$-2 = 2 \sin(30t)$

$-1 = \sin(30t)$

$30t = \sin^{-1} (-1) = \frac{3\pi}{2} + 2k\pi$, $k = 0,1,2, \cdots$

solve for $t$.

the max value of $T = 18.9 + 5.8 = 24.7$ so there is no $t$ satisfy $T(t) = 38$
I am sorry the appropriate value is 2, not 38, I will edit the original post.

$30t = \sin^{-1} (-1) = \frac{3\pi}{2} + 2k\pi$, $k = 0,1,2, \cdots$
I am lost as to how you got $\frac{3\pi}{2} + 2k\pi$.

I am also assuming (if you could please confirm) that k is referring to the cycles?

6. Originally Posted by Chris L T521
If d=3, then the first equation becomes $3=2\sin\!\left(30t\right)+5\implies 2\sin\!\left(30t\right)=-2\implies \sin\!\left(30t\right)=-1$.

To make it a little easier, let $\omega=30t$ so $\sin \omega=-1$. Now what values of $\omega$ cause this to be true? Take those value(s) and divide them by 30 to find t.

Can you try to do something similar for the second problem?
I ended up looking back on your solution and figured out the problem.

The answer given by the homework ended up being incorrect

But thank you so much for your help.