4.6 Graphs of other trig functions

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Graphing y = A tan(Bx - C), B > 0

1. Find two consecutive asymptotes by finding an interval containing one period -π/2 < Bx - C < π/2 2. Identify an x-intercept, midway between consecutive asymptotes. 3. Find the points ¼ and ¾ of the way between consecutive asymptotes 4. Graph one period.

Graphing y = A cot(Bx - C), B > 0

1. Find two consecutive asymptotes by finding an interval containing one period 0 < Bx - C < π 2. Identify an x-intercept, midway between consecutive asymptotes. 3. Find the points ¼ and ¾ of the way between consecutive asymptotes. 4. Graph one period.

Graph of y = sec x

Period is 2π, even function, undefined at π/2, domain: all real numbers except odd multiples of π/2, range: (-∞, -1] ∪ [1, ∞)

Graph of y = csc x

Period is 2π, odd function, undefined at π, domain: all real numbers except integral multiples of π, range: (-∞, -1] ∪ [1, ∞)

Graph of y = cot x

Period is π, odd function, undefined at π, domain: all real numbers except integral multiples of π, range: (-∞, ∞)

Graph of y = tan x

Period is π, odd function, undefined at π/2, domain: all real numbers except odd multiples of π/2, range: (-∞, ∞)


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