Aim: What are the graphs of tangent function and reciprocal functions?

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. 0.58 y 0 1 1.73 5.67 11.43 u.d. HW: Handout

2. y = tan x

3. 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) = tanx Domain: real numbers, and , k is integer} Range: { real numbers} Period: πwithin 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 isπ/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 = 2sinx 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 of 1. 2. 3.