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Study Notes

Trigonometry: Relationships between angles and ratios of lengths

Trigonometry is a branch of mathematics concerned with relationships between angles and ratios of lengths.
The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.
Throughout history, trigonometry has been applied in areas such as geodesy, surveying, celestial mechanics, and navigation.
Trigonometry is known for its many identities, which are commonly used for rewriting trigonometrical expressions to simplify an expression, find a more useful form of an expression, or solve an equation.
Sumerian astronomers studied angle measure, using a division of circles into 360 degrees.
In the 3rd century BC, Hellenistic mathematicians such as Euclid and Archimedes studied the properties of chords and inscribed angles in circles, and they proved theorems equivalent to modern trigonometric formulae.
The Greeks focused on the calculation of chords, while mathematicians in India created the earliest-known tables of values for trigonometric ratios such as sine.
The modern sine convention is first attested in the Surya Siddhanta, and its properties were further documented by the 5th century (AD) Indian mathematician and astronomer Aryabhata.
Driven by the demands of navigation and the growing need for accurate maps of large geographic areas, trigonometry grew into a major branch of mathematics.
Trigonometric ratios are the ratios between edges of a right triangle, which define functions of this angle that are called trigonometric functions.
Trigonometric functions were among the earliest uses for mathematical tables.
Trigonometry has been noted for its many identities, that is, equations that are true for all possible inputs.Trigonometry: Laws, Formulas, and Identities
The Law of Cosines extends the Pythagorean theorem to arbitrary triangles.
The Law of Tangents is an alternative to the Law of Cosines for solving unknown edges of a triangle.
The area of a triangle can be calculated using the product of two sides and the sine of the angle between them.
Heron's formula can also be used to calculate the area of a triangle.
Pythagorean identities are related to the Pythagorean theorem and hold for any value.
Euler's formula produces analytical identities for sine, cosine, and tangent in terms of e and the imaginary unit i.
Other commonly used trigonometric identities include the half-angle identities, the angle sum and difference identities, and the product-to-sum identities.

Description

Test your knowledge on trigonometry with this quiz that covers the relationships between angles and ratios of lengths. From the history of trigonometry to the various laws, formulas, and identities, this quiz will challenge your understanding of this important branch of mathematics. Whether you're a student learning about trigonometry for the first time or a math enthusiast looking to test your skills, this quiz is sure to provide a fun and educational experience. So, are you ready to show off your trigonometry knowledge