Derivatives of Trig Functions: Applications

1. Find the slope of the tangent to the curve y = x^{2} – sin^{2} x at x = 2.

2. For the equation y = 3cosx, find the minimum and maximum points.

3. The displacement of a particle is given by s = 2t sec t^{1/2}. Determine the velocity of the particle at t = 0.04.

4. A weight which is connected to a spring moves so that its displacement is:

x = sin 2t + 3^{1/2}cos 2t

What is its maximum displacement.

5. A V-shaped trough is to be constructed with sides that are 200cm long and 30 cm wide. Find the angle between the sides that maximizes the capacity of the trough.

Solution