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Understanding Trigonometric Functions: Tan, Cot, Csc, Sec

Explore the characteristics of tan, cot, csc, and sec functions, including asymptotes, x-intercepts, vertex shapes, and graph transformations. Learn how the graphs change with varying coefficients. Access examples to visually understand the concepts.

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Understanding Trigonometric Functions: Tan, Cot, Csc, Sec

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  1. Other Trigonometric Functions y = tan x Passes thru (0,0); increases from left to right; has asymptotes @ 90, 270, … y = cot x X-intercepts @ 90, 270; decreases from left to right; has asymptotes @ 0, 180, 360, …

  2. y = csc x has asymptotes @ 0, 180, 360, …; vertex of u-shape @ 1 and -1 y = sec x Crosses the y-axis; has asymptotes @ 90, 270, …; vertex of u-shape @ 1 and -1

  3. y = 7 tan x y = tan x By including a number for a, the graph becomes narrower. (If the a value is less than 1, the graph would be wider)

  4. y = 3 csc x y = csc x By including a number for a, the graph becomes narrower. (If the a value is less than 1, the graph would be wider). ALSO on sec and csc, the vertex of the graph shifts to ± a. (keep in mind if there is also a vertical shift that will move the graph up/down accordingly)

  5. Examples: Graph + 3 Graph

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