1. 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
π/6
π/4
π/3
4π/9
17π/36
π/2
0.58 y 1
1.73
5.67
11.43
u.d.
HW: Handout

2. y = tan x

3. Summary of the properties of f(x) = 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
, k is integer}
Range: {
real numbers}
Period: π within which lies 1 complete curve
Range: there is no range existed.
Vertical asymptotes: at odd multiples of π/2

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

5. y = tan 0.5x
Period is 2 π
y = tan 0.25x
Period is 4π

6. The general formula to find the period of tangent function is

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

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

9. 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.

10. 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.

11. 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

12. If f(x) = 2tan 2x, what is the value of1. 2. 3.