rules of trigonometry
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Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles. It has a set of rules and formulas that help in solving problems related to triangles. Here are some fundamental rules of trigonometry:
Right Triangle Definitions:
Hypotenuse: The side opposite the right angle in a right triangle. Denoted by 'c'.
Opposite side: The side opposite to a given angle. Denoted by 'a'.
Adjacent side: The side adjacent to a given angle. Denoted by 'b'.
Trigonometric Functions:
Sine (sin): The ratio of the length of the opposite side to the hypotenuse.
Cosine (cos): The ratio of the length of the adjacent side to the hypotenuse.
Tangent (tan): The ratio of the length of the opposite side to the adjacent side.
Pythagorean Identity:
In a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b):
c^2 = a^2 + b^2
Trigonometric Identities:
Sine and Cosine:
sin^2θ + cos^2θ = 1
Tangent and Secant:
tan^2θ + 1 = sec^2θ
Cotangent and Cosecant:
1 + cot^2θ = csc^2θ
Trigonometric Ratios:
Sine: sin(θ) = Opposite / Hypotenuse
Cosine: cos(θ) = Adjacent / Hypotenuse
Tangent: tan(θ) = Opposite / Adjacent
Cosecant: csc(θ) = 1 / sin(θ)
Secant: sec(θ) = 1 / cos(θ)
Cotangent: cot(θ) = 1 / tan(θ)
Periodicity:
Trigonometric functions are periodic, meaning they repeat their values after certain intervals. For example, sin(θ) and cos(θ) have a period of 2π radians or 360 degrees.
These are some of the fundamental rules of trigonometry. By using these rules, you can solve various problems involving angles and sides of triangles.
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