Sin, cos, and tan waves could not be represented graphically until after the invention of the Cartesian coordinate system by Descartes and the French mathematician Pierre de Fermat in 1637. Hipparchus’ work was referenced by Ptolemy over 250 years later, and so it’s not known why he didn’t derive the sine law of refraction himself. The ancient Greek astronomer Hipparchus created the first documented table of sine functions before 125 BCE. Tan( θ) = opposite length / adjacent length In the triangle above, sin( C) would equal length c / length c, which equals 1.
The sine of 90° is 1 because the opposite length will also be the longest, the hypotenuse. In Figure 2.3, sin( A) = length a / length c The sine of an angle ( θ) equals the ratio of two lengths - the length opposite the angle, and the longest length, the hypotenuse. The sine function shows how the angle inside a triangle changes as the lengths of its sides change. Reflection, Refraction, and DiffractionĢ0.