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Graphs of Secant and Cosecant

Graphs of Secant and Cosecant. Section 4.5b. The graph of the secant function. Wherever cos ( x ) = 1, its reciprocal sec( x ) is also 1. The graph has asymptotes at the zeros of the cosine function. The period of the secant function is , the same a s the cosine function.

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Graphs of Secant and Cosecant

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  1. Graphs of Secant and Cosecant Section 4.5b

  2. The graph of the secant function Wherever cos(x) = 1, its reciprocal sec(x) is also 1. The graph has asymptotes at the zeros of the cosine function. The period of the secant function is , the same as the cosine function. A local maximum of y = cos(x) corresponds to a local minimum of y = sec(x), and vice versa.

  3. The graph of the secant function

  4. The graph of the cosecant function Wherever sin(x) = 1, its reciprocal csc(x) is also 1. The graph has asymptotes at the zeros of the sine function. The period of the cosecant function is , the same as the sine function. A local maximum of y = sin(x) corresponds to a local minimum of y = csc(x), and vice versa.

  5. The graph of the cosecant function

  6. Summary: Basic Trigonometric Functions Function Period Domain Range

  7. Summary: Basic Trigonometric Functions Function Asymptotes Zeros Even/Odd None Odd None Even Odd Odd None Even None Odd

  8. Guided Practice Solve for x in the given interval  No calculator!!!  Third Quadrant Let’s construct a reference triangle: –1 Convert to radians: 2

  9. Whiteboard Problem Solve for x in the given interval  No calculator!!!

  10. Whiteboard Problem Solve for x in the given interval  No calculator!!!

  11. Guided Practice Use a calculator to solve for x in the given interval.  Third Quadrant The reference triangle: 1 1.5 Does this answer make sense with our graph?

  12. Guided Practice Use a calculator to solve for x in the given interval. Possible reference triangles: 0.3 -1 1 -0.3 or

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