How To sketch the graph of C and label relevant points?

Question

A curve C is given by parametric equations x=sect and y=tant, where 0<=t<pi/2

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Answer 1 · 2018-07-24T18:49:57

We can rewrite as follows:

$x^2 = sec^2t = tan^2t + 1$

Now solve for $tant$ .

$x^2 - 1 = tan^2t$

$tant = +- sqrt(x^2 - 1)$

Now you can substitute :

$y = +- sqrt(x^2 - 1)$

This is an easy relation to plot now.

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Hopefully this helps!