Warmup:
Use your calculator to complete the table for
cotangent below (we can do this without a calculator,
too). Make sure your calculator is in degree mode
and round to 1 decimal place. Then, graph the
function.
COTANGENT
cot x
tan
cot x
tan
2
1.5 1 0.5 0 ­0.5 ­1 ­1.5 ­2
0 30 60 90 120 150 180 210 240 270 300 330 360 1
2
3
How does changing the amplitude and
period affect the tangent and cotangent?
y = tan x
y = 2 tan x
y = cot x
y = cot 4x
4
Example 1
y = cot 2x
Amp:
Period:
x-scale:
List transformations:
5
Example 2
y = 3tan(½x-π)
Amp:
Period:
x-scale:
List transformations:
6
Example 3
Amp:
Period:
x-scale:
y = -4 cot (2πx + 3π/2)
List transformations:
7
How do you use sine & cosine
graphs to graph cosecant and
secant functions?
y = sin x
y = csc x
8
How do you use sine & cosine
graphs to graph cosecant and
secant functions?
y = cos x
y = sec x
9
How does changing the amplitude and
period affect the secant and cosecant?
y = csc x
y = sec x
y = 3 csc x
y = sec (3x)
10
Example 1
y = 4 csc x
Amp:
Period:
x-scale:
List transformations:
11
Example 2
y = sec (4x -
Amp:
Period:
x-scale:
) + 1
List transformations:
12
Example 3
y = -3 csc 4
Amp:
Period:
x-scale:
(x + 3) - 2
8
List transformations:
13
Homework
p. 341
#2,3,5,9-13,16,17,
21,22,27,28,29,30
14