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Trigonometry |
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Half angle formulas |
Trigonometric functions expressed by the
cosine of the double angle |
Trigonometric identities,
examples |
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Half angle formulas |
Using
the identities in which trigonometric functions are expressed by
the half angle, |
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and
applying the definitions of the functions, tangent and cotangent |
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Trigonometric functions expressed by the
cosine of the double angle
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Replacing a/2
by a
in the above identities, we get
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Trigonometric
identities
examples |
Example:
Prove the identity |
![](TrigEx19.gif) |
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Example:
Prove the identity |
![](TrigEx20.gif) |
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Example:
If tan
a
= 3/4, find tan
a/2.
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Solution:
Use formula |
![](TrigEx21.gif) |
to express tan
a/2
in terms of tan
a. |
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![](TrigEx21A.gif) |
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Example:
Prove the identity |
![](TrigEx22.gif) |
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Solution:
Substitute |
![](TrigEx22A.gif) |
then |
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![](TrigEx22B.gif) |
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Example:
Express the given
difference sin
61° -
sin 59° as a product.
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Solution:
Since |
![](TrigEx23.gif) |
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![](TrigEx23A.gif) |
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Example:
Prove the identity sin a
+ sin (a
+ 120°) +
sin (a
+ 240°)
= 0.
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Solution:
Applying the sum formula to
the last two terms on the left side of the identity we get,
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![](TrigEx24.gif) |
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Example:
Prove the identity |
![](TrigEx25.gif) |
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Solution:
Using the formula for the sum of the tangent |
![](TrigEx25A.gif) |
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![](TrigEx25B.gif) |
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Example:
Prove that |
![](TrigEx26.gif) |
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Solution: Replace
sin a
by cos (p/2
-
a)
and cos a
by sin (p/2
-
a)
and use the sum to product
formula
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![](TrigEx26A.gif) |
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Trigonometry
contents A |
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