# Lesson Product of trigonometric functions - Examples

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## Product of trigonometric functions - Examples

The formulas for the product of trigonometric functions formulas are:

,

,

.

The proofs of these formulas are presented in the lesson Product of trigonometric functions in this module.
Below are examples of application of these formulas.

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

Solution
First, calculate sin(15°). Use the product formula for sines-sines:
.

Take = 15°. You have
= (1/2)*(cos(0°) - cos(30°)) = ,
hence
sin(15°) = .

Compare this with the formula
sin(15°) = ,
which was obtained in the lesson Addition and subtraction formulas - Examples in this module.

Let me show you that the number is equal to .

Indeed, the square of is equal to , exactly as the square of , so the original numbers are the same.

Now, calculate cos(15°). Use the product formula for cosines-cosines:
.

Take = 15°. You have
= (1/2)*(cos(0°) + cos(30°)) = ,
hence
cos(15°) = .

Compare this with the formula
cos(15°) = ,
which was obtained in the lesson Addition and subtraction formulas - Examples in this module.

Let me show you that the number is equal to .

Indeed, the square of is equal to , exactly as the square of , so the original numbers are the same.

Now, having ready expressions for sin(15°) and cos(15°), you can easily calculate tan(15°) as the fraction sin(15°)/cos(15°):
tan(15°) = .

Note that, as it was shown in the lesson Addition and subtraction formulas - Examples in this module,
.

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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.

 , , , , , . The lessons Addition and subtraction formulas and                      Addition and subtraction formulas - Examples

Addition and subtraction of trigonometric functions
 , , , , , . The lessons Addition and subtraction of trigonometric functions and                      Addition and subtraction of trigonometric functions - Examples

Product of trigonometric functions
 , , . The lessons Product of trigonometric functions and                                                    Product of trigonometric functions - Examples (this lesson)

Powers of trigonometric functions
 , , , . The lessons Powers of Trigonometric functions and                                                             Powers of Trigonometric functions - Examples

Trigonometric functions of multiply argument
 , , , . The lessons Trigonometric functions of multiply argument and                                                                 Trigonometric functions of multiply argument - Examples

Trigonometric functions of half argument
 , , , , , . The lessons Trigonometric functions of half argument and                   Trigonometric functions of half argument - Examples

Miscellaneous Trigonometry problems

The lesson Miscellaneous Trigonometry problems

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