Algebra &Trigonometry
§ 7.5 - Review
Sullivan & Sullivan, Fourth Edition
Page 1 / 5
Establishing Double & Half Angle Formulas (Review)
1) Establish the identity for sin 2   2 sin  cos , using the Presentation Format below. Use the
sum formula ( sin      sin  cos   sin  cos  ) in order to do this
Establish that sin
Starting Point:
sin 2 
 1+1=2
2   2 sin  cos
= sin    
 Use the sum formula
=
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=

=
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=
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=
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Algebra &Trigonometry
§ 7.5 - Review
Sullivan & Sullivan, Fourth Edition
Page 2 / 5
Establish the identity for cos2   cos 2   sin 2  , using the Presentation Format below. .
Use the sum formula ( cos     cos  cos   sin  sin  ) in order to do this
2)
2   cos 2   sin 2 
Establish that cos
Starting Point:
cos2 
 1+1=2
= cos   

=

=

=

=

=

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
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Algebra &Trigonometry
§ 7.5 - Review
Sullivan & Sullivan, Fourth Edition
Page 3 / 5
1  cos 
 
3) Show that the following is true: cos  
.
2
2
We're going to do this in a slightly different manner than we normally do for establishing identities –
1  cos 
 
instead of taking one side of cos  
(which we haven't yet shown to be true), we're
2
2
instead going to take a different, already-known-to-be-true identity, and change that until it looks
1  cos 
 
like cos  
. Since we known that cos2   2 cos 2   1 is true, we can treat this like
2
2
an equation, and write the whole thing on each line. The 'trick' to this proof is to, change θ to α by
A
saying that   , and then isolating sine on one side.
2
1  cos 
 
Establish that cos  
2
2
Starting Point: cos2   2 cos 2   1













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Algebra &Trigonometry
§ 7.5 - Review
Sullivan & Sullivan, Fourth Edition
Page 4 / 5
1  cos 
 
4) Show that the following is true: sin   
.
2
2
We're going to do this in a slightly different manner than we normally do for establishing identities –
1  cos 
 
instead of taking one side of sin   
(which we haven't yet shown to be true), we're
2
2
instead going to take a different, already-known-to-be-true identity, and change that until it looks
1  cos 
 
like sin   
. Since we known that cos2   2 cos 2   1 is true, we can treat this like
2
2
 
an equation, and write the whole thing on each line. The 'trick' to this proof is to use a
A
Pythagorean identity to change the cos2 into a sin2., change θ to α by saying that   , and then
2
isolating sine on one side.
1  cos 
 
Establish that sin   
2
2
Starting Point: cos2   2 cos 2   1












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Algebra &Trigonometry
§ 7.5 - Review
Sullivan & Sullivan, Fourth Edition
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