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)

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Presentation transcript:

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)

Section 4-5: Graphing Other Trigonometric Functions

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

Section 4-5: Graphing Other Trigonometric Functions

Examples:

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

Section 4-5: Graphing Other Trigonometric Functions

Examples:

Section 4-5: Graphing Other Trigonometric Functions

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

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