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Graphs of the Cosecant, Secant, & Cotangent Functions

Objectives: Graph the secant, cosecant, & cotangent functions. Graph the transformations of the cosecant, secant, & cotangent graphs. Graphs of the Cosecant, Secant, & Cotangent Functions. 7.2. Graph of the Cosecant Function.

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Graphs of the Cosecant, Secant, & Cotangent Functions

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  1. Objectives: • Graph the secant, cosecant, & cotangent functions. • Graph the transformations of the cosecant, secant, & cotangent graphs. Graphs of the Cosecant, Secant, & Cotangent Functions 7.2

  2. Graph of the Cosecant Function Recall that the cosecant function is the reciprocal of the sine function. Therefore, wherever the sine function outputs 0, the cosecant function is undefined and a vertical asymptote is formed. The blue graph is the sine function & the red graph the cosecant function.

  3. Example #1 • List the transformation & sketch the graph. Vertical stretch by a factor of 2, x-axis reflection.

  4. Graph of the Secant Function Recall that the secant function is the reciprocal of the cosine function. And just like the sine function, whenever the cosine function outputs 0, the secant function is undefined and a vertical asymptote is formed. The blue graph is the cosine function & the red graph the cosecant function.

  5. Example #2 • List the transformation & sketch the graph. Vertical stretch by a factor of 3, vertical shift of 2 units up.

  6. Graph of the Cotangent Function • Cotangent is the reciprocal of the tangent function.

  7. Example #3 • List the transformation & sketch the graph. Vertical stretch by a factor of 4, x-axis reflection, horizontal shift of units left.

  8. Characteristics of the Reciprocal Trigonometric Functions

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