4.6 Graphs of other trig functions
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: (-∞, ∞)
