trigonometry
Trigonometry is the branch of mathematics that studies the quantitative relationships between the angles and sides of a triangle. It defines and analyzes trigonometric functions such as \(\sin x\), \(\cos x\), and \(\tan x\), which express these relationships in continuous form and extend beyond the geometric triangle to describe periodic and circular behavior.
The law of sines states that in any triangle, the ratio of each side to the sine of its opposite angle is constant and equal to the diameter of the triangle’s circumcircle.
The law of cosines states that, in any triangle, the square of one side is equal to the sum of the squares of the other two sides, minus twice their product multiplied by the cosine of the included angle:
\[
c^2 = a^2 + b^2 – 2ab \cos(\theta)
\]
Trigonometric equations are equations in which the unknown appears as the argument of trigonometric functions. There are various types of such equations, each with its corresponding solution method.
The sine function \(f(x) = \sin(x) \) assigns to each angle \(x\), expressed in radians, its corresponding sine value
The secant function \(f(x) = \sec(x)\) is defined as the reciprocal of the cosine function. It assigns to each angle \(x\) the value \(1/\cos(x)\).
The cosecant function \(f(x) = \csc(x) \) is defined as the reciprocal of the sine function. It assigns to each angle x (measured in radians) the value \( 1/\sin(x) \).