Math 1316
Section 4.3 Class Notes
Graphs of the Tangent and Cotangent Functions
1
Math 1316
Section 4.3 Class Notes
2
Math 1316
Section 4.3 Class Notes
Examples: Graph each function over a one-period interval.
Exercise 7 page 174: y  f ( x)  tan 4 x .
x
y = tan (4x)
3
Math 1316
Section 4.3 Class Notes
Exercise 13 page 174: y  f ( x)  cot 3x .
x
y = cot (3x)
4
Math 1316
Section 4.3 Class Notes
Exercise 27 page 174: y  f ( x)  1  2 tan x .
x
y = tan x
y = 2tan x
y = -1 + 2tan x
5
Math 1316
Section 4.3 Class Notes


Exercise 31 page 174: y  f ( x)  1  2 cot 2 x   .
2

x


y  f ( x)  cot 2 x  
2



y  f ( x)  2 cot 2 x  
2



y  f ( x)  1  2 cot 2 x  
2

6
Math 1316
Section 4.3 Class Notes
Graphs of the Secant and Cosecant Functions
7
Math 1316
Section 4.3 Class Notes
Examples: Graph each function in two-period interval.
1
Exercise 5 page 183: y  f ( x)  3 sec x .
4
x
y = cos (1/4x)
y = 3cos (1/4x)
8
Math 1316
Section 4.3 Class Notes
1
Exercise 6 page 183: y  f ( x)  2 sec x .
2
x
y = cos (1/2x)
y = -2cos (1/2x)
9
Math 1316
Section 4.3 Class Notes
10
Math 1316
Section 4.3 Class Notes


Exercise 8 page 183: y  f ( x)  csc x   .
4

x


y  csc x  
4

11
Math 1316
Section 4.3 Class Notes
1 

Exercise 9 page 183: y  f ( x)  csc x   .
2 
2
x


y  csc x  
4

1 

y  csc x  
2 
4
12