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| Trigonometry |
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Half angle formulas |
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Trigonometric functions expressed by the
cosine of the double angle |
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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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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 |
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| Example:
Prove the identity |
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Example:
If tan
a
= 3/4, find tan
a/2.
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| Solution:
Use formula |
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to express tan
a/2
in terms of tan
a. |
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| Example:
Prove the identity |
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| Solution:
Substitute |
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then |
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Example:
Express the given
difference sin
61° -
sin 59° as a product.
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| Solution:
Since |
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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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| Example:
Prove the identity |
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| Solution:
Using the formula for the sum of the tangent |
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| Example:
Prove that |
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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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| Trigonometry
contents A |
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| Copyright
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