Sine and Cosine

Let us learn about Sine and Cosine :

This relationship is expressed by the two most fundamental equations of trigonometry:

x = r × cos θ
y = r × sin θ

Or, equivalently:

cos θ = x/r
sin θ = y/r

Sin (sine) is the ratio of the vertical side (the side opposite the corner we're looking at) to the hypotenuse. Cos (cosine) is likewise the ratio of the horizontal side (the side adjacent to that corner) to the hypotenuse. Sine and cosine are functions, which is to say that they take one number (an angle in this case, usually expressed in degrees or radians) and spit out another. For certain values of θ, it is easy to figure out what the sine and cosine values are going to be just by thinking about what the angle corresponds to on the circle; the simplest cases are for θ = 0°, which is a line pointing right, giving cos θ = 1 and sine θ = 0; a line pointing straight up (ie. θ = 90°), which gives us cos θ = 0 and sine θ = 1, and so on. At 45° the opposite and adjacent sides are the same length, so from Pythagoras' Theorem (r2=x2 + y2) they must each be (√2)/2. For values in between the sine and cosine vary in a smooth curve, so that a plot of sin x against x is your basic wavy line:

Cosine is to sine as horizontal is to vertical, so the graph of cosine is just like the graph of sine shifted by one quarter-turn. On a graph together, they look like this:

Hope the above explanation helped you..