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Trigonometric functions and their reciprocals on the unit circle. All of the right-angled triangles are similar, i.e. the ratios between their corresponding sides are the same. For sin, cos and tan the unit-length radius forms the hypotenuse of the triangle that defines them.
A periodic function, also called a periodic waveform (or simply periodic wave), is a function that repeats its values at regular intervals or periods. The repeatable part of the function or waveform is called a cycle. [1] For example, the trigonometric functions, which repeat at intervals of radians, are
Basis of trigonometry: if two right triangles have equal acute angles, they are similar, so their corresponding side lengths are proportional.. In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) [1] are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
Point P(x,y) on the circle of unit radius at an obtuse angle θ > π/2 Sine function on unit circle (top) and its graph (bottom) The unit circle centered at the origin in the Euclidean plane is defined by the equation: [2] + = Given an angle θ, there is a unique point P on the unit circle at an anticlockwise angle of θ from the x-axis, and ...
Travelling a greater distance in the same time means a greater speed, and so linear speed is greater on the outer edge of a rotating object than it is closer to the axis. This speed along a circular path is known as tangential speed because the direction of motion is tangent to the circumference of the circle. For circular motion, the terms ...
In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. [ 1 ] [ 2 ] In other words, it is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, troughs, or zero crossings .
Given two sides a and b and the angle between the sides C, the area of the triangle is given by half the product of the lengths of two sides and the sine of the angle between the two sides: [85] Area = Δ = 1 2 a b sin C {\displaystyle {\mbox{Area}}=\Delta ={\frac {1}{2}}ab\sin C}
In the original theorem, the domain of the function f is the unit n-sphere (the boundary of the unit n-ball). In general, it is true also when the domain of f is the boundary of any open bounded symmetric subset of R n {\displaystyle \mathbb {R} ^{n}} containing the origin (Here, symmetric means that if x is in the subset then - x is also in ...