# How to graph tan and cot

## Graphs of Sine, Cosine and Tangent

Graphing Trigonometric Functions, Phase Shift, Period, Transformations, Tangent, Cosecant, Cosine

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Index of lessons Print this page print-friendly version Find local tutors. Sections: The sine and cosine , The tangent, The co-functions. The next trig function is the tangent, but that's difficult to show on the unit circle. The tangent will be zero wherever its numerator the sine is zero. The tangent will be undefined wherever its denominator the cosine is zero. Thinking back to when you learned about graphing rational functions , a zero in the denominator means you'll have a vertical asymptote. Let's put dots for the zeroes and dashed vertical lines for the asymptotes:.

If you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Skill Summary Legend Opens a modal. The graphs of sine, cosine, and tangent. Introduction to amplitude, midline, and extrema of sinusoidal functions.

Try this with the Unit Circle. A complete repetition of the pattern of the function is called a cycle and the period is the horizontal length of one complete cycle.
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In this lesson we are going to learn how to graph the other four trigonometric functions: tan, cot, sec, and csc. Well, it is any place where there is a gap or a break in our graph, meaning we are indicating any place where our function is undefined, as nicely stated by Interactive Mathematics. All of these functions are built from sine and cosine, and they all have denominators! And because they all have denominators, that means we need to make sure we never divide by zero! The awesome thing about these two graphs, is that all we really have to do is graph their reciprocal functions first i. 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.

Easy to understand trigonometry lessons on DVD. Try before you commit. However, they do occur in engineering and science problems. They are interesting curves because they have discontinuities. For certain values of x , the tangent, cotangent, secant and cosecant curves are not defined, and so there is a gap in the curve. Consider the denominator bottom of this fraction.

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