A function that depends on the value of an angle. One way to define it is with a unit circle (a circle with center in the coordinate origin, and radius of 1). To the right is zero, from there, a positive angle is counterclockwise. In this case, the sine is simply the y-coordinate, and the cosine is the x-coordinate of the point on the circle where the ray of the angle crosses the circle. The value of the sine (and cosine) obviously depends on the angle - that's why it is considered a "function".
Sine, cosine, tangent, cotangent, cosecans, and secans can also be defined via right triangles; for more details see here: http://en.wikipedia.org/wiki/Sine#Sine.2C_cosine_and_tangent
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The Fourier series is a specific type of infinite mathematical series involving trigonometric functions that are used in applied mathematics. It makes use of the relationships of the sine and cosine functions.
sine 810 = sine 90 = 1
Sine(A+ B) = Sine(A)*Cosine(B) + Cosine(A)*Sine(B).
Sine 3.3 degrees is about 0.057564. Sine 3.3 radians is about -0.157746. Sine 3.3 grads is about 0.051813.
sine 45 = 0.850903525