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 11.43 u.d.

HW: Handout

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x

y

y = tan x

The sine and cosine curves are continuous while the graph of y = tan x is not – or discontinuous at

2,

2

3,

2

xxx

etc

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and the graph repeats everyπ

x k 2

2 1( )

y

Summary of the properties of f(x) = tan xDomain:

real numbers, and

, k is integer}real numbers}

xx{

Range: {

Period: π within which lies 1 complete curve

Range: there is no range existed.

Vertical asymptotes: at odd multiples of π/2

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x

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y = 2 tan x

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Period is π

y = 2 tan 2x

Period is π/2

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y = tan 0.5x

Period is 2 π

y = tan 0.25x

Period is 4π

The general formula to find the period of tangent function is

B

a) Graph: y = 2sin x and y = tan x on the same axes, over

x

.

b) How many values are the solutions of tan x = 2sin x?Math Composer 1. 1. 5http: / / www. mathcomposer. com

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5 points

y = 2sin x

y = tan x

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y = cot x

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

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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.

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

y = csc x

What are the maximum and minimum values of the function

a) y = 3 sin 2x ?

b) y = 3 cos 2x ?

c) y = 3 tan 2x ?

a) Max. = 3, Min. = -3

b) Max. = 3, Min. = -3

c) Max. is infinity, Min. is negative infinity

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

f ( ) ?4

1.

2. ?)3

3(

f

3. ?)2

(

f