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Example 4 from Algebra and Trigonometry, 8.2 Graphs of the Other Trigonometric Functions
Graphing a Variation of the Secant Function
Graph one period of
Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.
Solution
- Step 1. The given function is already written in the general form,
- Step 2. so the stretching factor is
- Step 3. so The period is units.
- Step 4. Sketch the graph of the function
- Step 5. Use the reciprocal relationship of the cosine and secant functions to draw the cosecant function.
- Steps 6–7. Sketch two asymptotes at and We can use two reference points, the local minimum at and the local maximum at Figure 8 shows the graph.
Figure 8
Your turn
The book's Try It right after this example: same idea, new numbers. Only the answer is given.
Graph one period of
How did it go?