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.

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

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!