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Subtracting from both sides and dividing by 2 by two yields the power-reduction formula for sine: = ( ()). The half-angle formula for sine can be obtained by replacing θ {\displaystyle \theta } with θ / 2 {\displaystyle \theta /2} and taking the square-root of both sides: sin ( θ / 2 ) = ± ( 1 − cos θ ) / 2 ...
The angle opposite the leg of length 1 (this angle can be labeled φ = π/2 − θ) has cotangent equal to the length of the other leg, and cosecant equal to the length of the hypotenuse. In that way, this trigonometric identity involving the cotangent and the cosecant also follows from the Pythagorean theorem.
This screenshot shows the formula E = mc 2 being edited using VisualEditor.The window is opened by typing "<math>" in VisualEditor. The visual editor shows a button that allows to choose one of three offered modes to display a formula.
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.
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). The formulae sin 1 / 2 (a + b) and cos 1 / 2 (a + b) are the ratios of the actual distances to ...
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The specific weight, also known as the unit weight (symbol γ, the Greek letter gamma), is a volume-specific quantity defined as the weight W divided by the volume V of a material: = / Equivalently, it may also be formulated as the product of density, ρ, and gravity acceleration, g: = Its unit of measurement in the International System of Units (SI) is newton per cubic metre (N/m 3), with ...
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