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Trigonometry is a mathematical field that examines the relationships between triangle angles and sides, especially in right-angled triangles. It uses sine, cosine, and tangent functions to calculate unknown angles and distances. The mnemonic SOHCAHTOA aids in remembering these relationships, while the Laws of Sines and Cosines extend trigonometry to non-right-angled triangles. Additionally, the unit circle is a fundamental concept for understanding trigonometric functions and their periodic nature.
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Trigonometry is a branch of mathematics that explores the relationships between angles and sides of triangles
Sine, cosine, and tangent
The primary trigonometric functions, sine, cosine, and tangent, express the relationships between angles and sides of triangles as ratios
Reciprocal functions
The reciprocal functions, cosecant, secant, and cotangent, are the inverse of the primary trigonometric functions
Trigonometric functions are crucial for determining unknown angles and distances in right-angled triangles
The Laws of Sines and Cosines are used to solve for unknown sides and angles in general triangles
The formula for calculating the area of any triangle is (1/2)ab sin(C), where 'a' and 'b' are the lengths of the sides and 'C' is the measure of the included angle
The unit circle is a circle with a radius of one unit centered at the origin of a coordinate plane, used to represent trigonometric functions and understand their properties
Trigonometric functions can be represented as coordinates on the unit circle, with the x-coordinate corresponding to the cosine of an angle and the y-coordinate to the sine
The unit circle provides insight into the periodic nature of trigonometric functions and their values at various angles