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Q: How are sines and cosines used in meteorology?

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Trigonometric ratios, by themselves, can only be used for right angled triangles. The law of cosines or the sine law can be used for any triangle.

Trigonometry mainly but also geometry, algebra.

It's an infinite sum of sines and cosines that can be used to represent any analytic (well-behaved, like without kinks in it) function.

For a start, try converting everything to sines and cosines.

The ACT asks questions about basic sines, cosines, and tangents. These questions can be answered without a calculator.

Law of sines or cosines SinA/a=SinB/b=SinC/c

Use Law of Sines if you know:Two angle measures and any side length orTwo side lengths and a non-included angle measure.Use Law of Cosines if you know:Two side lengths and the included angle measure orThree side lengths.

Every periodic signal can be decomposed to a sum (finite or infinite) of sines and cosines according to fourier analysis.

When none of the angles are known, and using Pythagoras, the triangle is known not to be right angled.

Having sufficient angles or sides one can use either, The Law of Sines, or, The Law of Cosines. Google them.

No. Sines are well defined trigonometric ratios whereas "this" is not defined at all.

The Fourier series can be used to represent any periodic signal using a summation of sines and cosines of different frequencies and amplitudes. Since sines and cosines are periodic, they must form another periodic signal. Thus, the Fourier series is period in nature. The Fourier series is expanded then, to the complex plane, and can be applied to non-periodic signals. This gave rise to the Fourier transform, which represents a signal in the frequency-domain. See links.

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