1 6 Graphs of Other Trigonometric Functions Part

1. 6 Graphs of Other Trigonometric Functions Part 2

Now, Cotangent Graphs! Very similar to the tangent function It also has a period of π.

Now, Cotangent Graphs! l Recall that: l We now have to consider when sin x has value zero, because this will determine where our asymptotes should go. l sin x = 0, when x = π, so the asymptotes will occur at x = nπ (Any multiple of π)

Vertical asymptotes are where sin x = 0 (multiples of π) Period π Domain: all x ≠nπ Range (-∞, ∞)

Graph of the Cotangent function For comparison:

Sketch the graph of y = 2 cot(x/3) l l x Solve the equations: x/3 = 0 and x/3 = π x = 0 and x = 3π You can see that two consecutive asymptotes occur at x = 0 and x = 3π Between these asymptotes, plot a few points, including the x-intercept. Make a table of these values: 3π/4 y = 2 cot(x/3) 2 3π/2 9π/4 0 -2

x 3π/4 3π/2 9π/4 y = 2 cot(x/3) 2 0 -2 graph of y = 2 cot(x/3) Asymptotes at x = 0 and x = 3π (3π/4, 2) (3π/2, 0) (9π/4, -2)

Example: Describe Transformation of y = cot x for f(x) = 3 cot(x/2) + 1 l Horizontal stretch by a factor of 2. A vertical stretch by a factor of 3. Up 1 unit. l The horizontal stretch makes the period 2π. l The asymptotes: Solve the equations: x/2 = 0 and x/2 = π x = 0 and x = 2π You can see that two consecutive asymptotes occur at x = 0 and x = 2π l l

Graph of f(x) = 3 cot(x/2) + 1 [-2π, 2π] by [-10, 10]

Classwork: l 1. 6 Practice Worksheet – The Tangent and Cotangent Graph

Homework l l Pg 179 9 – 12; 21, 22, 24, 25, 30, 47