Warm-up 04/22/2012
1. How does the graph of y1 = sinx transform in order to form
the graph of y2 = -2∙sinx?
2. The function h(t) = 4cos(πt) models the height of a buoy, in
feet, as a function of time. What is the maximum height
the buoy reaches? What is the minimum height that the
buoy reaches?
3. For the buoy described in #2, how often will the buoy be at
sea level? Or, in other words, how often will the buoy’s
height be 0?
4. Evaluate sec x   2 for x on [0,2π].
For #’s 5 – 8, identify the quadrant:
5. sinx < 0 and tanx > 0
6. cosx < 0 and cscx > 0
7. tanx < 0 and sinx > 0
8. secx < 0 and cscx > 0
9. Evaluate sin(x) = 1 without using a calculator for x on [0,2π]
 15 
csc
10.
What is the exact value for the  4  ?


Chapter 4 Section 5 (Part 1)
The Graphs of Secant and Cosecant
Explore!
Be sure your graphing calculator is in radian mode. Also, switch
the zoom to “ZTrig” using the zoom button.
1. Graph y = sinx. Describe the calculator’s viewing window.
In other words, in what increments are each of the axes
divided up into? What are the viewed domain and the
viewed range on the calculator screen?
2. Now, graph y = cscx along with y = sinx. In order to do this,
1
csx

note that
sin x . How can the graph of y = sinx be
used to obtain that of y = cscx?
3. Now, graph y = cosx and y = secx in the same viewing
screen. How can the graph of y = cosx be used to obtain
that of y = secx?
4. Make a prediction! If you want to graph either
y = acsc(bx ± c) ± d or y = asec(bx ± c) ± d, what could you
do in order to obtain the graph?
Examples: Sketch a graph of each of the following:
1. y= ½sec(2x – π)
2. y = -csc(¼x) + 2
Assignment: text p.401 #1, 3, 7, 8, 11, 12, 15, 16, 23, 26, 29, 30,
32, 33, 54, 55, and graph the following four equations along
with their corresponding reciprocal equation:


y

2
csc
x




4

 y = sec2x
 y = -2csc4x + 2
x



 y  3 sec 2  2 


1