Evaluating Integral with $\theta(t)$ - Sin | Cos

[Pi-Bond]

Suppose I know the value of an integral:

\int_0^T cos(\theta)dt = x

Is there any way to evaluate the integral \int_0^T sin(\theta)dt solely from this information?

EDIT: \theta=\theta(t), i.e. \theta is a function of t.

 

[pmsrw3]

Well, you can get the absolute value.

<br /> \begin{eqnarray*}<br /> \int_0^T \cos(\theta) dt = T \cos(\theta) = x \\<br /> \cos(\theta) = x/T \\<br /> \cos^2(\theta) + \sin^2(\theta) = 1 \\<br /> sin(\theta) = \pm\sqrt{1-\cos^2(\theta)} \\<br /> \int_0^T \sin(\theta) dt = T \sin(\theta) \\<br /> \end{eqnarray*}<br />

Should be obvious from there.

 

[Pi-Bond]

Unfortunately, I omitted a key piece of information in my original post - \theta is a function of t, i.e. \theta=\theta(t). Is there any way then?

 

[pmsrw3]

Nope!