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In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles. According to the law, = = =, where a, b, and c are the lengths of the sides of a triangle, and α, β, and γ are the opposite angles (see figure 2), while R is the radius of the triangle's circumcircle.
Fig. 1 – A triangle. The angles α (or A), β (or B), and γ (or C) are respectively opposite the sides a, b, and c.. In trigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths of the sides of a triangle to the cosine of one of its angles.
Euclid proved that the area of a triangle is half that of a parallelogram with the same base and height in his book Elements in 300 BCE. [1] In 499 CE Aryabhata, used this illustrated method in the Aryabhatiya (section 2.6). [2] Although simple, this formula is only useful if the height can be readily found, which is not always the case.
In this right triangle: sin A = a/h; cos A = b/h; tan A = a/b. Trigonometric ratios are the ratios between edges of a right triangle. These ratios depend only on one acute angle of the right triangle, since any two right triangles with the same acute angle are similar. [31]
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. The reciprocal identities arise as ratios of sides in the triangles where this unit line is no longer the hypotenuse.
The cross product is defined by the formula [8] [9] ... The cross product can be used to calculate the normal for a triangle or ... the moment M of a force F B ...
The given formula is for the plane passing through the center of mass, which coincides with the geometric center of the cylinder. If the xy plane is at the base of the cylinder, i.e. offset by d = h 2 , {\displaystyle d={\frac {h}{2}},} then by the parallel axis theorem the following formula applies:
basic physics formula triangles: Image title: Image mnemonics in the style of the Ohm's law formula triangle for high-school physics by CMG Lee. Covering the unknown in each mnemonic gives the formula in terms of the remaining parameters. In the SVG file, hover over a symbol for its meaning and formula. Width: 100%: Height: 100%