4. Applications: Derivatives of Trigonometric Functions
by M. Bourne
We can now use derivatives of trigonometric and inverse trigonometric functions to solve various types of problems.
Find the equation of the normal to the curve of `y=tan^-1x/2` at `x=3`.
The apparent power Pa of an electric circuit whose power is P and whose impedance phase angle is θ, is given by
`P_a = P\ sec\ θ`.
Given that P is constant at 12 W, find the time rate of change of Pa if θ is changing at the rate of 0.050 rad/min, when θ = 40.0°.
A machine is programmed to move an etching tool such that the position of the tool is given by x = 2 cos 3t and y = cos 2t, where the dimensions are in cm and time is in s. Find the velocity of the tool for t = 4.1 s.
The television screen at a sports arena is vertical and 2.4 m high. The lower edge is 8.5 m above an observer's eye level. If the best view of the screen is obtained when the angle subtended by the screen at eye level is a maximum, how far from directly below the screen must the observer be?
A winch on a loading dock is used to drag a container along the ground. The winch winds the cable in at 2ms-1 and is 5 m above the ground. At what rate is the angle θ between the cable and the ground changing when 10 m of cable is out?