Name _____________________________________
Lesson 10.1 Notes
Date ___________
Mrs. Chiarenza
Period ______
Graphs in Trigonometry
Do Now:
Fill in the table below for the function y = sin x.
Next we will plot all of these points on a graph.
Guidelines for graphing all curves:
1. We are going to hold the graph paper sideways
2. For this example we only need the quadrants I and IV (only where x is positive, since we
started at zero.)
3. If you notice, the numbers on the table are very large. They go up to 360º and could go
further. Because of this we are ALL going to use the same intervals for EVERY graph no
matter the table.
For the X- AXIS : ________________________________________________________
For the Y-AXIS : ________________________________________________________
The sine curve is a _____________________ curve that passes through _________.
Next, do the same thing for the cosine function.
The cosine curve is a _____________________ curve that passes through _________.
Transforming Trig Graphs
The general form of a trig equation is:
where a is the _____________________ of the function.

The amplitude tells you ___________________________________________________.

The ______________ of a sine or cosine function is always _______________________.
For example, the graph of y = 3 sin x looks like:
Also, in the general forms:
b is the _____________________ of the function.

The frequency tells you ___________________________________________________.

The ______________ of a sine or cosine function is given by _____________________.

The period tells you ______________________________________________________.
Complete sine curve
Complete cosine curve
So the graph of the equation y = cos 2x looks like:
Example: State the amplitude, range, frequency, and period of each function.
1. y = 3 sin 2x
2. y = cos(-4)x

3. y = sin x
4. y = -2 sin (1/2) x
3
6. y  cos x
2
7.

y  4 sin
5. y = 2 cos 3x
1
x
2
1
8. y  cos2x
3

Graphing Sine and Cosine Curves
Example: Graph y = sin 2x on the interval 0° ≤ x ≤ 360º.
1. Start by labeling _________________________________________________________.
2. You will _____________________________, but to do this you have to _____________
________________________. (It will not always be 90º.) To tell what you will count
by, ____________________________.
If _____________ count by __________.
If _____________ count by __________.
If _____________ count by __________.
3. Also remember if ____________________________, you must ____________________
_______________________________________________________________________.
Now let’s create a table for the example above: y = sin 2x.
|a| =
R:
b=
p=
Graphing Trig Functions on the Calculator
1. _______________________________________________________________________.
2. Hit ______________ for the trig graph. (Notice that it shows you ___________________
so you may only be graphing half of it on your graph paper - _______________________
______________________________!)
3. To see the table with the values you want you must hit ___________________________.
You want ______________ (because _____________________________). You must
change _________________________________________________________________.
4. To see the table, hit ______________________________.
Now draw and label the axes, plot the points, and draw the curve!
Example: Graph y = (1/2)cos 3x on the interval -π ≤ x ≤ π
(Notice here that _______________________________, which means _____________________
______________________________! For this, we have to ______________________________
______________________________________. Make the top row and the bottom row as usual,
and in the middle row, __________________________________________________________.
|a| =
R:
b=
p=
Practice: Graph each function on the given interval.
1. y = 2 cos x on the interval 0° ≤ x ≤ 360°.
|a| =
R:
b=
p=
2. y = sin 2x on the interval -180° ≤ x ≤ 180°.
|a| =
R:
b=
p=
3. y = 3 cos 2x on the interval 0 ≤ x ≤ 2π.
|a| =
R:
b=
p=
3
4. y  cos 3x on the interval 0° ≤ x ≤ 360°.
2
|a| =

R:
b=
p=