Section 4.5b Graphs of Secant and Cosecant. The graph of the secant function The graph has asymptotes at the zeros of the cosine function. Wherever cos(x)

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Presentation transcript:

Section 4.5b Graphs of Secant and Cosecant

The graph of the secant function The graph has asymptotes at the zeros of the cosine function. Wherever cos(x) = 1, its reciprocal sec(x) is also 1. 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.

The graph of the secant function

The graph of the cosecant function The graph has asymptotes at the zeros of the sine function. Wherever sin(x) = 1, its reciprocal csc(x) is also 1. 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.

The graph of the cosecant function

Summary: Basic Trigonometric Functions FunctionPeriodDomainRange

Summary: Basic Trigonometric Functions FunctionAsymptotesZerosEven/Odd NoneOdd NoneEven Odd None Even Odd

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

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

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

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

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