__Category__: Differential Calculus, Trigonometry"Published in Newark, California, USA"

If an angle θ increases uniformly, find the smallest positive value of θ for which tan θ increases 8 times as fast as sin θ.

__Solution__:

The given word problem is about the rate problem of an angle θ and its trigonometric functions.

From the word statement, "...for which tan θ increases 8 times as fast as sin θ." then the working equation will be

Take the derivative on both sides of the equation with respect to time t as follows

As you notice that we can cancel the angular rate which is

^{d}

^{θ}/

_{dt}on both sides of the equation and we can solve for the value of angle θ as follows

Take the cube root on both sides on the equation, we have

Take the inverse cosine on both sides of the equation,

Therefore,