### Sine Wave

Transcript: For "opposite" and the "adjacent" side (tangent), etc. To define the trigonometric functions for an acute angle A, start with any right triangle that contains the angle A. The three sides of the triangle are named as follows: The adjacent side is the side that is in contact with (adjacent to) both the angle we are interested in (angle A) and the right angle, in this case side b. The hypotenuse is the side opposite the right angle, in this case side h. The hypotenuse is always the longest side of a right-angled triangle. The opposite side is the side opposite to the angle we are interested in (angle A), in this case side a. In trigonometry, a unit circle is the circle of radius one centered at the origin (0, 0) in the Cartesian coordinate system. Let a line through the origin, making an angle of θ with the positive half of the x-axis, intersect the unit circle. The x- and y-coordinates of this point of intersection are equal to cos θ and sin θ, respectively. The point's distance from the origin is always 1. Unlike the definitions with the right or left triangle or slope, the angle can be extended to the full set of real arguments by using the unit circle. This can also be achieved by requiring certain symmetries and that sine be a periodic function. History Small help to remember trigonometric functions Sine Wave By Michal Pocinek Geometry Tangent where a, b, and c are the lengths of the sides of a triangle, and A, B, and C are the opposite angles (see the figure to the right), and D is the diameter of the triangle's circumcircle. When the last part of the equation is not used, sometimes the law is stated using the reciprocal: Sine Law Sine wave for my project SOH: Sinus, opposite hypotenuse The following are examples of how to solve a problem using the law of sines: Given: side a = 20, side c = 24, and angle C = 40° Using the law of sines, we conclude that While the early study of trigonometry can be traced to antiquity, the trigonometric functions as they are in use today were developed in the medieval period. The law of sines can be used to compute the remaining sides of a triangle when two angles and a side are known—a technique known as triangulation. However calculating this may result in numerical error if an angle is close to 90 degrees. It can also be used when two sides and one of the non-enclosed angles are known. In some such cases, the formula gives two possible values for the enclosed angle, leading to an ambiguous case. The law of sines is one of two trigonometric equations commonly applied to find lengths and angles in a general triangle, with the other being the law of cosines. -Sine wave can be imagined as a sea wave -It have infinity of possible ways to draw it. -Working with sine wave we use : The first published use of the abbreviations 'sin', 'cos', and 'tan' is by the 16th century French mathematician Albert Girard In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of an arbitrary triangle to the sines of its angles. According to the law, Cosinus Right angle triangle CAH Cosinus, adjacent / hypotenuse Sinus is not the only function used to calculate the sides in a triangle. It can not be used every time so there are other two functions. All of these three functions can be used only in the right angle triangle. In mathematics, the sine function is a trigonometric function of an angle. The sine of an angle is defined in the context of a right triangle: for the specified angle, it is the ratio of the length of the side that is opposite that angle to (divided by) the length of the longest side of the triangle (i.e. the hypotenuse). SOH CAH TOA Point P(x,y) on the circle of unit radius at an obtuse angle θ > π/2 What is Sine Wave? Exaple for trigiometric function Use in Mathematics An geometric waveform that oscillates (moves up, down or side-to-side) periodically, and is defined by the function y = sin x. In other words, it is an s-shaped, smooth wave that oscillates above and below zero. The Opus palatinum de triangulis of Georg Joachim Rheticus, a student of Copernicus, was probably the first in Europe to define trigonometric functions directly in terms of right triangles instead of circles, with tables for all six trigonometric functions; this work was finished by Rheticus' student Valentin Otho in 1596. The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. In our case does not depend on the size of the particular right triangle chosen, as long as it contains the angle A, since all such triangles are similar. Unit circle TOA tangent, opposite / adjacent