Pg. 335 Homework
• Pg. 346 #1 – 14 all, 21 – 26 all
Study Trig Info!!
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#45
#47
#49
#51
#53
#55
 2  2
,
2
2
3 1
,
2 2
Proof
+,+,+
–,–,+
3 1
, , 3
2 2
1
,
2
1
,
2
3
2
3
2
#46
#48
#50 Proof
#52 + , – , –
#54 – , + , –
#56 21 ,  2 3 , 33
6.3 Graphs of sin x and cos x
The Unit Circle
• The Unit Circle can help us
graph each individual
function of sin x and cos x
by looking at the unique
output values for each input
value. This gives us a
domain and range.
• Look at your Unit Circle.
What do you notice about
the input and output
values?
• The graph of sin x.
• The graph of cos x.
6.3 Graphs of sin x and cos x
sin x and cos x together
• Where do they intersect?
How do you know?
• Where do the maximums
and minimums of the
graphs occur?
• What is the domain?
Range?
• Graph:
y = sin x
y = 2sin x
y = 3sin x
In the same window. What
do you notice?
6.3 Graphs of sin x and cos x
Amplitude
• Graph:
y = cos x
y = -2cos x
In the same window. What
do you notice?
• The amplitude of
f(x) = asin x and f(x) = acos x
is the maximum value of y,
where a is any real number;
amplitude = |a|.
Period Length
• Graph:
y = sin x
y = sin (4x)
y = sin (0.5x)
In the same window. What
do you notice?
• One period length of
y = sin bx or y = cos bx is
2
b
6.3 Graphs of sin x and cos x
Horizontal Shifts
• Remember our cofunctions
and why they were true?
Well, they are true with
graphing too!
• The cofunctions lead into
shifts. If a value is inside
with the x, it is a horizontal
shift left or right opposite
the sign. If it is outside the
trig, it is up or down as the
sign states.
Symmetry of sin x and cos x
• Looking at the Unit Circle to
help, think about the
difference between the
following:
 
 
sin   and sin   
4
 4
 5 
 5 
cos 
and
cos



 6 
 6 
• sin (-x) = -sin (x)
• cos (-x) = cos (x)
6.3 Graphs of sin x and cos x
Examples 
Graph the following:
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y = 4sin x
y = -3cos (2x)
y = sin (0.5x) + 1
y = 2sin (x – 1)
Solve for the following:
• sin x = 0.32 on 0 ≤ x < 2π
• cos x = -0.75 on 0 ≤ x < 2π
• sin x = -0.14 on 0 ≤ x < 2π
• cos x = 0.65 on 0 ≤ x < 2π