Q5 of 64 Page 135

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

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 .


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