# How do you graph ##y=-3 sec x##?

Draw ##y=-1/3cosx## first and then draw its reciprocal graph. The reciprocal graph is ##y=-3secx##.
Of course, if you can use a graphic calculator you just type your equation in and let the calculator draw the graph for you.
But if you can’t, draw the reciprocal function of ##y=-1/3cosx##, I assume you know how to draw the reciprocal function.
If you don’t, draw ##y=-1/3cosx## ‘s graph first, should not be very hard, ##1/3## is the amplitude and when ##x=0## ##y## is ##-1/3## apparently. The period is ##2π##, don’t forget to draw it periodically.
graph{ -1/3cosx [-10, 10, -5, 5]}
##y_1=-1/3cosx##
graph{ -3secx [-10, 10, -5, 5]}
##y_2=-3secx##
graph{(y+3secx)(y+1/3cosx)=0 [-36.53, 36.5, -18.26, 18.27]}
##y_1## and ##y_2## graphs in one set of coordinates.
As you can see, every time the graph ##y_1=-1/3cosx## touche x-axis, ##y_2=-3secx## has a vertical asymptote. For other values, the product of these two is always 1.(for example, when##x=0,y_1=-1/3## and ##y_2=-3##, their product is 1. This applies to every point on these two graphs, so according to this if you know how to draw ##y=-1/3cosx##, you know how to draw its reciprocal ##y=-3secx##.)

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