All two other basic ratios can be defined in terms of sine, as follows:cosine = sqrt(1 - sine2)
and then
tangent = sine/cosine.
You need to know the quadrant of the angle to determine whether these ratios are positive or negative.
The cosecant, secant and cotangent ratios are simply reciprocals and so easily derived from the above definitions.
cosecant
The basic functions of trigonometry are: sine cosine tangent secant cosecant cotangent
in trigonometry
Trigonometry
It is the reciprocal of the sine ratio.
Using its Taylor-series.
The sine of one of the acute angles in a right triangle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.
Yes, because all sound waves can be modelled as sine (or cosine) waves, or combinations of sine waves.
sine, cosine, tangent, cosecant, secant, cotangent.
Electromagnetic radiation is propogated as sine waves.
You could try the series sin(x) = 1 - x/1! + x^3/3! - x^5/5! + ... but you would soon need a calculator. And if you're using a calculator you may as well use it to find the sine.
If you have a right triangle, the sine of an angle is the ratio of the opposite side to the hypotenuse.