1. Section 4.5b Graphs of Secant and Cosecant

2. 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.

3. The graph of the secant function

4. 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.

5. The graph of the cosecant function

6. Summary: Basic Trigonometric Functions FunctionPeriodDomainRange

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

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

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: 1.5 1 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 or -0.3 1