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pre-calc 4.6 - Section 4.6 Graphs of Other Trigonometric...

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Section 4.6 Graphs of Other Trigonometric Functions In this section, we look at the graphs of other trigonometric functions. We use the traditional symbol x , rather than θ or t , to represent the independent variable. We use the symbol y for the dependent variable, or the function’s value at x . So we are looking at graphs of y = tan x , y = cot x, y = csc x, and y = sec x in the rectangular coordinate system. In all graphs of trigonometric functions, the independent variable, x , is measured in radians. Properties of tangent: Period is π. Tangent function is odd: tan (-x) = - tan x The graph is symmetric with respect to the origin. Tangent is undefined at π/2 so there is a vertical asymptote at π/2 The Graph of y = tan x Graph y = tan x by listing some points on the graph. Since the period of sine is 2π, graph the function on [0, π/2) and complete the graph on the interval (-π/2, π/2) using the fact that the function has origin symmetry. The rest of the graph is made up of repetitions of this portion. x 0 6 π 4 π 3 π 12 5 π 36 17 π 180 89 π y = tan x 0 3 3 ≈0.6 1 3 ≈1.7 3.7 11.4 57.3 You can get a more complete graph of y =tan x by continuing the portion shown above to the left and to the right over intervals of π.
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Characteristics of the tangent function The domain is all real numbers except odd multiples of π/2 The range is (-∞, ∞), the set of all real numbers. The period is π. (The graph’s pattern repeats in every interval of length π.) The function is an odd function with origin symmetry.
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