Name________________________________________________________
Date_________
Graphing the Sine and Cosine Functions
10H Per_____
Warm-Up: Draw a unit circle diagram with the quadrantal angles in radian measure. Use it to fill in the table of values
for sin  and cos  .
Radian
0

2

3
2
2
sin 
cos 
The sine function represents the height of any point on the unit circle. Therefore, the graph of the sine function will
relay that information to the reader.
Ex. 1: Graph y  sin  (using the values from the unit circle or table) over 0    2 .
a) State the domain and range of y  sin  in interval notation.
b) Extend the graph over the interval  2    2 .
c) After how much horizontal distance will the sine function repeat its basic pattern?
This is called the _____________of the trigonometric graph. Because these graphs have patterns that repeat they are
called ____________.
d) Based on the graph of y  sin  over  2    2 , is the sine function even, odd, or neither? Why?
e) Over the interval  2 , 2  , list the following information for y  sin  :
i. All relative extrema (max and min)
ii. All intervals for which y  sin  is increasing
iii. All intervals for which y  sin  is decreasing
iv. All x-intercepts
v. The end behavior
The sine function looks like a wave that passes through the _____________.
The cosine function represents the width of any point on the unit circle. Therefore, the graph of the cosine function will
relay that information to the reader.
Ex. 2: Graph y  cos  (using the values from the unit circle or table) over 0    2 .
a) State the domain and range of y  cos  in interval notation.
b) Extend the graph over the interval  2    2 .
c) What is the period of y  cos  ?
d) Based on the graph of y  cos  over  2    2 , is the cosine function even, odd, or neither? Why?
e) Over the interval  2 , 2  , list the following information for y  cos  :
i. All relative extrema (max and min)
ii. All intervals for which y  cos  is increasing
iii. All intervals for which y  cos  is decreasing
iv. All x-intercepts
v. The end behavior
The cosine function looks like a wave that passes through the point __________________.
The _______________ of a function is half the distance between the __________ and ___________ values of the
function.
What is the amplitude of y  sin  from example 1? How about y  cos  from example 2?
How do you think the graph of y  sin  will change if the amplitude is:
Increased?
Decreased?
Ex. 3: Graph the function y = 2sinx over 0  x  2 .
Negated?
What is the domain and range of y = 2sinx?
Homework:
1. Graph the function y = 3sinx over  2  x  2 .
a) What is the domain and range of
y = 3sinx?
b) What are the coordinates of the
relative maximum?
c) What is the relative minimum?
d) What is the relative minimum value?
e) Is y = 3sinx even, odd, or neither? Why?
f)
Describe the end behavior.
2. Graph the function y = 3cosx over 0  x  2 .
a) What is the domain and range of
y = 3cosx?
b) What are the coordinates of the
relative minimum?
c) What is the relative maximum?
d) What is the relative maximum value?
e) Is y = 3cosx even, odd, or neither? Why?
f)
Describe the end behavior.