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If the ratios are equivalent the corresponding points will all be on the same straight line through the origin.
According to Math experts, Hipparchus, Menelaus, and Ptolemy are responsible for developing Greek trigonometry for the purposes of studying differences in shapes of the planets, sun and moon. By observing the shapes of each, they were able to determine the ratios and areas of each one.
it originally came from the ancient Egyptian and babylonian times as it is seen in there scriptures as i kind of mathematic way to work with triangles
In advanced mathematics, familiar trigonometric ratios such as sine, cosine or tan are defined as infinite series. For example, sin(x) = x - x3/3! + x5/5! - ... Such series are used to calculate trig ratios and the proof of their their convergence to a specific value depends on calculus.
plane trigonometry spherical trigonometry