$\begingroup$ @robjohn: OK fair enough, I wasn't really trying to define sine and cosine so much as I was trying to point out that radians are usually introduced via the arclength of a wedge, not the area of a wedge (divided by 2). Also, I didn't have a problem with using that...
The numbers in a sequence are referred to as terms. The terms of a triangular sequence are related to the number of dots needed to create a triangle. You would begin forming a triangle with three dots; one on top and two on bottom. The next row would have three dots, making a total ...
We can derive a simple factor to convert from radians to degrees by noting that a circle has 360 degrees and that the circumference of the circle is 2πr units in length. When a radial line traces an entire circle, the arc length is 2πr/r = 2π, and since the line traces an ang...
g form formula value trigonometric ratio √3 / 2 0.8660254037 circular system pi/6 or π/6 0.8660254037 centesimal system cos 33 (⅓) g 0.8660254037 cos 30 degrees proof now that you know the value of cos 30 degrees, let’s explore how to derive this value. we will study the two ...
side of a right triangle the adjacent side is the remaining side where it forms a side of both the angle of interest and the right angle the cosine function of an angle is equal to the length of the adjacent side divided by the length of the hypotenuse side and the formula is given ...
It takes him only a couple of pages of very light mathematics to derive the standard kinetic theory formula for the pressure of an ideal gas: He’s implicitly assuming a certain randomness to the motions of the molecules, but he barely mentions it (and this particular ...
A polygon is any closed two-dimensional figure with 3 or more straight (not curved) sides, and a 12-sided polygon is known as a dodecagon. A regular dodecagon is one with equal sides and angles, and it's possible to derive a formula for calculating its area. An irregular dodecagon has...
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Despite the widespread use of prescribed fire throughout much of the southeastern USA, temporal considerations of fire behavior and its effects often remain unclear. Opportunities to burn within prescriptive meteorological windows vary seasonally and alo
(*Check that there are two triangles, if not we are on a boundary and we will then ignore them in the calculation*) If[Length[cc] == 2, (* Calculate the position in the list of Triangles where the two triangles attached to the line between i ...