# Lesson Trigonometric functions of half argument - Examples

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## Trigonometric functions of half argument - Examples

The formulas for the Trigonometric functions of half argument are:

, ,

,

, , .

The proofs of these formulas are presented in the lesson Trigonometric functions of half argument in this module.
Below are examples of applications of these formulas.

Problem 1
Find sin(22°30'), sin(22°30'), tan(22°30').

Solution
First, calculate sin(22°30').
Since 22°30' = 45°/2=, you can apply the formula of half argument for sines (see the lesson Trigonometric functions of half argument in this module):
sin(22°30') = .

Similarly, cos(22°30') = .

Hence,
tan(22°30') = sin(22°30')/cos(22°30') = .

Example 2
Find cos(15°), sin(15°), tan(15°).

Solution
First, find sin(15°). Use the formula of half argument for sines (see the lesson Trigonometric functions of half argument in this module):
sin^2(15°) = (1-cos(30°)/2 = .

Hence,
sin(15°) = .

Now, find cos(15°). Use formula for cosines of half argument, which is the second formula in this lesson. You have

cos^2(15°) = (1+cos(30°)/2 = .

Hence,
cos(15°) = .

Consequently,
tan(15°) = sin(15°)/cos(15°) = .

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For your convenience, below is the list of my lessons on Trigonometry in this site in the logical order.
They all are under the current topic Trigonometry in the section Algebra II.

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Powers of trigonometric functions
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Trigonometric functions of multiply argument
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Trigonometric functions of half argument
 , , , , , . The lessons Trigonometric functions of half argument and                   Trigonometric functions of half argument - Examples (this lesson)

Miscellaneous Trigonometry problems

The lesson Miscellaneous Trigonometry problems

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