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The graph gets bigger and bigger rather than smaller because as the fractions in the cosine function get smaller their reciprocals in the secant function get bigger. The graph of the secant function is as follows.

What Are The Inverse Trigonometric Functions With Images

This lesson shows how to graph the reciprocal trigonometric functions y csc x y sec x and y cot x using the y sin x y cos x and y tan x functions.

How to graph csc functions. To graph a cosecant function we start with the sine graph by first determining the amplitude the maximum point on the graph the period the distance time for a complete oscillation the phase. The graph of cosine goes from 1 into fractions and all the way down to 0. After applying this concept throughout the range of x values we can proceed to sketch the graph of y sec x.

A sketch of the sine function. Secant takes the reciprocal of all these values and ends on this first interval at the asymptote. Since the graph of the function does not have a maximum or minimum value there can be no value for the amplitude.

If playback doesn t begin shortly try restarting your device. Draw the vertical asymptotes through the x intercepts as the following figure shows. First we graph y cos x and then y sec x immediately below it.

Find amplitude period and phase shift y csc x use the form to find the variables used to find the amplitude period phase shift and vertical shift. Once we have the reciprocal curves sketched all we have to do next is place vertical asymptotes anywhere the reciprocal graph crosses the center line. Compare the y values in each of the 2 graphs and assure yourself they are the reciprocal of each other.

Oh a vertical asymptote is a line that our function will approach but never touch or cross. Similarly csc θ csc theta csc θ is not defined for values of θ thetaθ such that sin θ 0 sin theta 0sin θ 0 which occurs for θ 0 kπ theta 0 k piθ 0 kπ for any integer kkk. Sketch the graph of y sin x from 4 π to 4 π as shown in this figure.

To graph y csc x follow these steps. Therefore the cosecant function has vertical asymptotes at these values of θ thetaθ. Draw y csc x between the asymptotes and down to and up to the.

It s behaves like boundary lines. Y cos x.