Pg. 346 Homework
• Pg. 346
#27 – 41 odd
Pg. 352
#7 – 12 all
Study Trig Info!! Next Quiz is Monday!
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#1
#3
#5
#7
#9
#11
#13
#21
#23
#25
max = 4, a = 4
max = 15, a = 15
max = 5, a = 5
D: ARN; R [-1, 1], 2π/3
D: ARN; R [-4, 4], 2π/5
D: ARN; R [-3, 3], π
D: ARN; R [-1, 1], 2π/3
[0, π] x [-2, 2]
[0, 4π] x [-3, 3]
[0, 10π] x [-4, 4]
#2
#4
#6
#8
#10
#12
#14
#22
#24
#26
max = 1, a = 1
max = 3, a = 3
max = 12, a = 12
D: ARN; R [-1, 1], 2π/7
D: ARN; R [-2, 2], 2π/9
D: ARN; R [-6, 6], 2π/9
D: ARN; R [1, 3], 2π
[0, 4π] x [-2, 2]
[0, 6π] x [-2, 2]
[0, 8π] x [-4, 4]
6.3 Graphs of sin x and cos x
Amplitude
• 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|.
• State the amplitude:
y = 4sin(6x)
y = -3cos(0.25x)
Period Length
• One period length of
y = sin bx or y = cos bx is
2
b
• State the period length:
y = 4sin(6x)
y = -3cos(0.25x)
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   
6
 6
 4 
 4 
cos 
and
cos



 3 
 3 
• sin (-x) = -sin (x)
• cos (-x) = cos (x)
6.3 Graphs of sin x and cos x
Examples 
Graph one period of 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
6.4 Graphs of the Other Trig Functions
Graphing tan x
• What are the values to
“worry about” with tan x?
• What does a function do at
a vertical asymptote?
• Graph tan x.
Period Length of tan x
• How long does it take for
tan x to take on all its
possible values?
• π!!