| 1. | The various trigonometric identities associated with the heptagonal triangle include these:
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| 2. | Therefore, this trigonometric identity follows from the Pythagorean theorem.
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| 3. | Then with a few trigonometric identities we reduce the equation to
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| 4. | Also, there are many ways to rewrite these formulas using trigonometric identities.
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| 5. | This is the case of distributivity or trigonometric identities.
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| 6. | We may substitute the first equation into the second and, using the trigonometric identity
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| 7. | Using the trigonometric identity and where \ cdot is the usual euclidean dot product.
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| 8. | There are arithmetic relations between these functions, which are known as trigonometric identities.
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| 9. | These are listed in List of trigonometric identities.
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| 10. | The three ball-based slimness factors can be calculated using well-known trigonometric identities.
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