Aim: How do we graph cot(x), sec(x) and csc(x)?
Objective: use the unit circle to derive the graph of cot(x), sec(x) and csc(x) and explore their features.
Lesson Development: Use the unit circle to plot the know values for cot(x), sec(x) and csc(x) on the interval,
[ 0,2 ]
Sec(x)
Csc(x)
Vertical asymptotes
x   n, n  Z
x

2
n, n  Z
Domain
All real values
except at
x   n, n  Z
All real values
except at
x
Cot(x)
x   n, n  Z
HW#4: P285 – 286: 7ab, 8ab, 9, 12, 20

n, n  Z
2
All real values
except at
x   n, n  Z
Range
1 y  
Period

  y  1
1 y  
  y  1

All real numbers

Solutions
P285 – 286:
7) a) x  n , n is any whole number
8) a) x  n
9)
12) has no solutions
20)
b) x 

2
 n
b) none
where n is any whole number