
Trigonometric
Functions and Their Graphs: Sections: The sine and cosine, The tangent, The cofunctions What about the cofunctions, the secant, the cosecant, and the cotangent? The cosecant is the reciprocal of the sine. Wherever the sine is zero, the cosecant will be undefined, so there will be a vertical asymptote. Wherever the sine reaches its maximum value of 1, the cosecant will reach its minimum value of 1; wherever the sine reaches its minimum value of –1, the cosecant will reach its maximum value of –1. Wherever the sine is positive but less than 1, the cosecant will be positive but greater than 1; wherever the sine is negative but greater than –1, the cosecant will be negative but less than –1.
By using the same reasoning with the cosine wave, I can create the secant graph: The Secant Graph The secant and cosecant have periods of length 2π, and we don't consider amplitude for these curves. The cotangent is the reciprocal of the tangent. Wherever the tangent is zero, the cotangent will have a vertical asymptote; wherever the tangent has a vertical asymptote, the cotangent will have a zero. And the signs on each interval will be the same. So the cotangent graph looks like this: The Cotangent Graph The cotangent has a period of π, and we don't bother with the amplitude. When you need to do the graphs, you may be tempted to try to compute a lot of plot points. But all you really need to know is where the graph is zero, where it's equal to 1, and / or where it has a vertical asymptote. If you know the behavior of the function at zero, π/2, π, 3π/2, and 2π, then you can fill in the rest. That's really all you "need". << Previous Top  1  2  3  Return to Index


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