Aim What are the graphs of tangent function

Aim: What are the graphs of tangent function and reciprocal functions? • Do Now: If y = tan x, fill in the table and then sketch the graph. x 0 π/6 π/4 π/3 4π/9 17π/36 π/2 y 0 0. 58 1 1. 73 5. 67 HW: Handout 11. 43 u. d.

y = tan x

The sine and cosine curves are continuous while the graph of y = tan x is not – or discontinuous at etc and the graph repeats everyπ , Summary of the properties of f(x) = tan x Domain: real numbers, and Range: { , k is integer} real numbers} Period: π within which lies 1 complete curve Range: there is no range existed. Vertical asymptotes: at odd multiples of π/2

y = 2 tan x Period is π y = 2 tan 2 x Period is π/2

y = tan 0. 5 x Period is 2 π y = tan 0. 25 x Period is 4π

The general formula to find the period of tangent function is

a) Graph: y = 2 sin x and y = tan x on the same axes, over b) How many values are the solutions of tan x = 2 sin x? y = tan x y = 2 sin x. 5 points

y = cot x For integral values of n, the vertical lines on the graph at x = nπ are asymptotes

y = sec x For integral values of n, every π/2 + nπ , sec x is undefined. The vertical lines on the graph at x = π/2 + nπ are asymptotes.

y = csc x For integral values of n, every nπ , csc x is undefined The vertical lines on the graph at x = nπ are asymptotes.

What are the maximum and minimum values of the function a) y = 3 sin 2 x ? b) y = 3 cos 2 x ? c) y = 3 tan 2 x ? a) Max. = 3, Min. = -3 b) Max. = 3, Min. = -3 c) Max. is infinity, Min. is negative infinity

If f(x) = 2 tan 2 x, what is the value of 1. 2. 3.