1. Section 4-5: Graphing Other Trigonometric Functions Since tan(x) = sin(x) / cos(x), the tangent function is undefined when cos(x) = 0. That means tan(x) has a vertical asymptote whenever cos(x) = 0. This also means that tan(x) has zeros wherever sin(x) = 0 ◦ (multiples of 0 and π)

2. Section 4-5: Graphing Other Trigonometric Functions

5. The general form of the tangent function is: y = a tan(bx + c) + d a creates vertical stretch/compression b affects period c produces phase shift d produces vertical shift

6. Section 4-5: Graphing Other Trigonometric Functions

7. Examples:

8. Section 4-5: Graphing Other Trigonometric Functions Examples: Locate the vertical asymptotes and sketch the graph of each function:

9. Section 4-5: Graphing Other Trigonometric Functions

10. Examples:

11. Section 4-5: Graphing Other Trigonometric Functions

14. Examples: Locate the vertical asymptotes and sketch the graph of each function:

15. Section 4-5: Graphing Other Trigonometric Functions Homework: Page 277 #3 – 24 every 3 rd problem #29, 31, 33