Warm-up
Graph the following and find the amplitude,
period, increment, sinusoidal axis, starting point,
domain, range, asymptotes (if necessary).
1) 4cot(3x - 2∏) + 1
2) -3cos(x/2+ ∏) - 3
Graphing Secant and Cosecant
Calculator Investigation
• Graph the following pairs of graphs on your
calculator two at a time.
– sin(x) and csc(x)
– 2sin(x) and 2csc(x)
– sin(x) – 3 and csc(x) – 3
– sin(2x - 2∏) and csc(2x - 2∏)
Notice things and be ready to discuss them.
Function
Y = sin(x)
y = csc(x)
Ratio Identity
Asymptotes
How to graph cosecant
1) Lightly graph sine as a guide function.
2) Draw asymptotes wherever the graph of sine
crosses the sinusoidal axis. (Why?)
3) Draw the cosecant graph using the
maximums and minimums of the sine graph.
4) Erase the sine graph.
Lets graph one together…
f(x) = -2csc(3x + ∏) – 4
…and also find the relative maximums, relative
minimums, asymptotes, period, increment, S.A.,
starting point, domain and range.
Lets graph another one together…
f(x) = -4sec(2x - 3∏) + 2
…and also find the relative maximums, relative
minimums, asymptotes, period, increment, S.A.,
starting point, domain and range.
Practice
Find the relative maximums, relative minimums,
asymptotes, period, increment, S.A., starting
point, domain and range and graph each
function:
Y=
Y=
𝜋
sec(x + )
3
𝜋
csc(x - )
2
Y = 2sin(2x
Y = cot(x/2
-1
𝜋
- )
2
𝜋
+ )
3
Y = -4tan(3x +
+1
𝜋
) +6
4