Question

consider the strophoid r = 2cos(theta)-sec(theta)

Answer 1

a) sketch the strophoid from\[-\pi/3\] to \[\pi/3\]


how do i sketch this without using graphing calculator...?

Answer 2

b) find the slope of the tangent to the strophoid in terms of \[\theta\]
at what points is the slope 0?
where is the slope infinite?


for the slope equation, i got \[(\sec^2\theta-2\cos2\theta)/2(\sin2\theta+\tan \theta)\]

however i dont know how to continue since i do not know how to solve
\[\sec^2\theta-2\cos2\theta\]......

Answer 3

A plot of interest from Mathematica is attached.

Answer 4

@robtobey thank you!. but can you please tell me how do to graph it using only pen and paper....i could not find any steps or examples in my textbook....

Answer 5

Sorry, no. That is what computers are for.

Answer 6

You have to plot \(r(\theta)=2\cos\theta-\sec\theta\) for \(-\dfrac{\pi}{3}\le\theta\le\dfrac{\pi}{3}\).

Pick some values of \(\theta\) that are easy to find the cosine and secant of, such as \(\pm\dfrac{\pi}{6}\), starting at one endpoint.