The second form of each equation is derived from the first by eliminating " ? " t using Snell's law and trigonometric identities.
32.
Also in the late 10th and early 11th centuries AD, the Egyptian astronomer Ibn Yunus performed many careful trigonometric calculations and demonstrated the following trigonometric identity:
33.
Which can be seen to hold for all integers, together with Euler's formula, implies several trigonometric identities as well as de Moivre's formula.
34.
It has been shown that Craig had notes on a method of Paul Wittich that used trigonometric identities to reduce a multiplication formula for the sine function to additions.
35.
Due to this relationship, a number of trigonometric identities and theorems that are known today were also known to Hellenistic mathematicians, but in their equivalent chord form.
36.
With typical constraints on the two amplitude modulation waveforms, quadrature modulation can result in a single constant-envelope, phase-modulated carrier described mathematically by the trigonometric identity:
37.
Substituting a \ cos t for x and b \ sin t for y in ( ) yields the basic trigonometric identity \ cos ^ 2 t + \ sin ^ 2 t = 1.
38.
That helps to bring the result into the form U + iV and keep it simple without needing to apply trigonometric identities .-- Talk 06 : 24, 29 November 2006 ( UTC)
39.
It can be proven ( see List of trigonometric identities ) that the envelope of the maxima and minima form a wave whose frequency is half the difference between the frequencies of the two original waves.
40.
In this case 2 + 1 / 2 is unlikely to be useful, but XX-YY = 1 is a familiar trigonometric identity . talk ) 19 : 55, 10 December 2008 ( UTC)
