Provide two examples of the use of the derivatives of trigonometric functions in

Question

Provide two examples of the use of the derivatives of trigonometric functions in solving engineering or technology related problems.

Explain these examples and relate them to electrical engineering / electronics

Choose one of your examples of the application of the derivative of trigonometric function in engineering technology and solve it.

Include a mathematically and verbally thorough description of the work to find the derivative and relative extrema of your example.

Describe the relevance of these relative extrema with respect to your technical application.

Include relevant graphs of your function and perhaps of its derivative.

To receive points, answer all parts must be answered. No scanned work either. I cannot view it

Explanation / Answer

1st example

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.

Answer

vx=dxdt=?6 sin 3t

vy=dydt=?2 sin 2t

At t=4.1, vx=1.579 and vy=?1.88.

So

v=(vx)2+(vy)2????????????=(1.579)2+(?1.88)2??????????????????=2.46 cm/s

For velocity, we need to also indicate direction. First, we find the appropriate acute angle (the "reference" angle):

?=tan?1(1.881.579)=50?

So since we are in the 4th quadrant when vx is positive and vy is negative, the required angle is 360??50?=310?

2nd example

Find the equation of the normal to the curve of y=tan?1x2 at x=3.

Answer

dydx=11+(x2)2(12)

When x=3, this expression is equal to: 0.153846

So the slope of the tangent at x=3 is 0.153846.

The slope of the normal at x=3 is given by:

?10.153846=?6.5

So the equation of the normal is given by:

(When x=3, y=0.9828)

y?0.9828=?6.5(x?3) or

y=?6.5x+20.483

example related to electrical engineerng

Given that P is constant at 12 W, find the time rate of change of Pa if ? is changing at the rate of 0.050 rad/min, when ? = 40.0

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