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Trigonometry is a branch of mathematics that deals with the relationships between triangle angles and sides, especially in right-angled triangles. It builds on Pythagoras' theorem, enabling the calculation of unknown angles and sides using trigonometric ratios: sine, cosine, and tangent. These ratios, encapsulated by the mnemonic SOHCAHTOA, are fundamental for solving mathematical problems involving triangles. The text also covers the use of inverse trigonometric functions to find missing angles and the importance of memorizing key values for manual problem-solving.

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## Trigonometry

### Definition of Trigonometry

Trigonometry is a branch of mathematics that studies the relationships between angles and sides of triangles

### Trigonometric Ratios

Sine, Cosine, and Tangent

The core of trigonometry lies in the trigonometric ratios, which are sine, cosine, and tangent, and are crucial for solving problems involving triangles

SOHCAHTOA

SOHCAHTOA is a mnemonic device used to remember the definitions of sine, cosine, and tangent

### Applications of Trigonometry

Trigonometry is used to find missing side lengths and angles in right-angled triangles, and can be practiced without a calculator by memorizing key values

## Pythagoras' Theorem

### Definition of Pythagoras' Theorem

Pythagoras' theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides

### Limitations of Pythagoras' Theorem

While Pythagoras' theorem is useful for finding missing side lengths in right-angled triangles, it does not account for angles

### Relationship between Pythagoras' Theorem and Trigonometry

Pythagoras' theorem is a fundamental concept in trigonometry and serves as a basis for expanding the mathematical toolkit to include angle-related calculations in any type of triangle