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SUMMARY: We talk about how to introduce your students to graphing trigonometric functions.

After you’ve explained to your students that the sine and cosine are functions from the real numbers to the real numbers, you may need to mention that the tangent, cotangent, secant, and cosecant are also functions of a real variable but that are undefined for some real numbers. Explain to them the reason for the undefinedness: these last four functions are defined as ratios, where their denominators are variables, which cannot be zero, so all the angles for which these ratios have denominators equal to zero need to be excluded. And those angles are the real numbers for which these functions are undefined. As you explain, you may need to remind them how these functions were defined in the rectangular coordinate system, and you may...

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