Find an angle which increases twice as fast as its sine.

Question

Philoid · Accepted Answer

Given: a condition

To find the angle θ such that it increases twice as fast as its sine.

Explanation: Let x = sin θ

On differentiating with respect to t, we get

Applying the derivative, we get

But it is given that

Substituting this value in equation (i), we get

Now cancelling the like terms, we get

1 = 2cos θ

But given , this is possible only when

Hence the angle θ is .