Search results
Results from the WOW.Com Content Network
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 function with period P will repeat on intervals of length P, and these intervals are sometimes also referred to as periods of the function. Geometrically, a periodic function can be defined as a function whose graph exhibits translational symmetry , i.e. a function f is periodic with period P if the graph of f is invariant under translation ...
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.
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 ...
The sign of the square root needs to be chosen properly—note that if 2 π is added to θ, the quantities inside the square roots are unchanged, but the left-hand-sides of the equations change sign. Therefore, the correct sign to use depends on the value of θ. For the tan function, the equation is:
The sides of this rhombus have length 1. The angle between the horizontal line and the shown diagonal is 1 / 2 (a + b).This is a geometric way to prove the particular tangent half-angle formula that says tan 1 / 2 (a + b) = (sin a + sin b) / (cos a + cos b).
More precisely, suppose that the point is moving on the curve at a constant speed of one unit, that is, the position of the point P(s) is a function of the parameter s, which may be thought as the time or as the arc length from a given origin. Let T(s) be a unit tangent vector of the curve at P(s), which is also the derivative of P(s) with ...
The trigonometric functions of angles that are multiples of 15°, 18°, or 22.5° have simple algebraic values. These values are listed in the following table for angles from 0° to 45°. [ 1 ] In the table below, the label "Undefined" represents a ratio 1 : 0. {\displaystyle 1:0.}