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The sine, cosine, and tangent ratios in a right triangle can be remembered by representing them as strings of letters, for instance SOH-CAH-TOA in English: Sine = Opposite ÷ Hypotenuse Cosine = Adjacent ÷ Hypotenuse Tangent = Opposite ÷ Adjacent
There are several equivalent ways for defining trigonometric functions, and the proofs of the trigonometric identities between them depend on the chosen definition. The oldest and most elementary definitions are based on the geometry of right triangles and the ratio between their sides.
For instance, a mnemonic is SOH-CAH-TOA: [34] Sine = Opposite ÷ Hypotenuse Cosine = Adjacent ÷ Hypotenuse Tangent = Opposite ÷ Adjacent. One way to remember the letters is to sound them out phonetically (i.e. / ˌ s oʊ k ə ˈ t oʊ ə / SOH-kə-TOH-ə, similar to Krakatoa). [35]
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A fifth column is a group of people who undermine a larger group or nation from within, usually in favor of an enemy group or another nation. The activities of a fifth column can be overt or clandestine. Forces gathered in secret can mobilize openly to assist an external attack. The term is also applied to organized actions by military personnel.
Influential works from the 4th–5th century AD, known as the Siddhantas (of which there were five, the most important of which is the Surya Siddhanta [23]) first defined the sine as the modern relationship between half an angle and half a chord, while also defining the cosine, versine, and inverse sine. [24]
Chng Suan Tze v. Minister for Home Affairs is a seminal case in administrative law decided by the Court of Appeal of Singapore in 1988. The Court decided the appeal in the appellants' favour on a technical ground, but considered obiter dicta the reviewability of government power in preventive detention cases under the Internal Security Act ("ISA").
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