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Understanding the Cosine Rule - Mathematics Stack Exchange
WEBMar 22, 2023 — The cosine rule is a generalization of the Pythagorean theorem. The Pythagorean theorem says that if the legs of a right triangle have lengths a a and b b, and the hypotenuse has length c c, then c2 =a2 +b2 c 2 = a 2 + b 2. However, this relationship holds only if the angle opposite the long side is a right angle; no other angle works.
Math.stackexchange.comVerifying the cosine rule - Mathematics Stack Exchange
WEBTriangle cannot be shown. Then use Cramer’s Rule to solve for cosC , and use the result to verify the Law of Cosines: c2 = a2 +b2 − 2abcos(C) c 2 = a 2 + b 2 − 2 a b c o s (C) algebra-precalculus. Share. Cite. edited Apr 20, 2014 at 20:59. Undergradstudent.
Math.stackexchange.comgeometry - How does law of cosines work with vectors?
WEBThere's lots of confusion with the minus sign because of the law for triangles. Take the following diagram: say, V1 is the vector from B to C, and V2 is the vector from C to A. C is the angle you want to use in the above vector formula ∥V3∥2 = ∥V1∥2 + ∥V2∥2 + 2∥V1∥∥V2∥ cos(θ). But the " θ " in that formula is actually θ
Math.stackexchange.comUse the law of cosines to derive the triangle inequality
WEBStack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Math.stackexchange.comTrigonometric ratios for angles greater than $90^\\circ$?
WEB7. There are two possible definitions of the trigonometric ratios: The trigonometric ratios can be defined for angles greater than 0∘ 0 ∘ and less than 90∘ 90 ∘ using right triangles. In particular, sin(θ) sin. . (θ) is defined as the ratio of the lengths of the opposite leg and the hypotenuse, and cos(θ) cos. .
Math.stackexchange.comCalculating Sum of 2 Vectors using Laws of Cosine
WEB1. I found this to calculate the sum of 2 vectors with a specific angle v v: It's the law of cosine: a2 +b2 − 2ab cos(v) a 2 + b 2 − 2 a b cos (v) Sources are split on this, however One source says the one above is the way to go, but others say this one is: a2 +b2 + 2ab cos(v) a 2 + b 2 + 2 a b cos (v)
Math.stackexchange.comtrigonometry - when to use sine vs cosine vs tangent
WEBFeb 14, 2014 — However it's a lot easier to find them directly given a standard right-angled triangle problem. For reference, the identities that you can use are: sin2 x +cos2 x tan2 x + 1 1 +cot2 x = 1 =sec2 x, where sec x = 1/ cos x =cosec2x, where cot x = 1/ tan x,cosecx = 1/ sin x sin 2 x + cos 2 x = 1 tan 2 x + 1 = sec 2 x, where sec x = 1 / cos x 1
Math.stackexchange.comHow to understand dot product is the angle's cosine?
WEB$\begingroup$ I think the cosine comes from the cosine rule and not the compound angle formula. Given 2 vectors $\vec{a}$ and $\vec{b}$ emanating from the same point. Given the angle between them and the fact that the vector opposite the angle is $\vec{b}-\vec{a}$ you can use the cosine rule and derive the formula for the dot product. $\endgroup$
Math.stackexchange.comtrigonometry - Does the Law of Sines and the Law of Cosines …
WEBThe law of cosines applied to right triangles is the Pythagorean theorem, since the cosine of a right angle is $0$. $$ a^2 + b^2 - \underbrace{2ab\cos C}_{\begin{smallmatrix} \text{This is $0$} \\[3pt] \text{if } C\,=\,90^\circ. \end{smallmatrix}} = c^2. $$ Of course, you can also apply the law of cosines to either of the other two angles.
Math.stackexchange.comTrouble understanding sine, cosine of angles greater than
WEBFeb 5, 2019 — When trigonometric functions like sine and cosine are applied to situations where we're dealing with angles that are greater than or equal to 90 degrees, the logic based purely on the right triangle definition of trigonometric functions as we know it breaks because in elementary trigonometry the sum of the angles in a right triangle (or any …
Math.stackexchange.com