S
ECT
5.6 T
RIGONOMETRIC
I
DENTITIES
PART
2
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D
OUBLE
A
NGLE
I
DENTITIES
Verify the identities Numerically with:
The identity
is valid
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P
ROVING
THE
D
OUBLE
A
NGLE
I
DENTITIES
To prove the Double Angle Identities, use the “Sum Identities”
Ex: Prove
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P
RACTICE
: P
ROVE
THE
FOLLOWING
I
DENTITIES
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U
SING
D
OUBLE
A
NGLE
I
DENTITIES
TO
S
OLVE
E
QUATIONS
Ex: Solve the following equation for
0
≤ θ
≤
360°
Note: You are “Solving for
θ
”,
not proving an identity!!
Use the Double-Angle Identity
Factor the equation
Solve for
θ
from each equation.
Remember to use CAST and there
are TWO cycles between 0 and
360°
Add the period
(
180°)
to find
other solutions
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P
RACTICE
: S
OLVE
FOR
0
≤
Θ
≤
360°
Use the Double-Angle Identity
Factor: Difference of Square
Solve for
θ
from each equation.
Remember to use CAST
Note: There is only ONE cycle
Between 0 and
360°
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P
ROOFS
USING
D
OUBLE
A
NGLE
I
DENTITIES
Use the Double-Angle Identity
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P
RACTICE
: P
ROVE
THE
FOLLOWING
I
DENTITIES
Multiply top &
bottom by:
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C
HALLENGE
: P
ROVE
Sum Identities
Use the Double Angle Identities
for “
sin2x”
& “
cos2x”
Expand/Distribute
Combine like-terms
Pythagorean Identity
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C
HALLENGE
:
Graph the following equation without a graphing calculator.
Find the amplitude, period, vertical and horizontal shifts
First: Simplify the equation
using the Double Angle Identity
Amplitude:
Period:
Vertical shift:
x
y
1
2
3
4
5
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H
OMEWORK
:
P342
# 5, 6, 10, 13, 16, 17, 19, 24, 26 27 - 29
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