Okays, lessee:
First off, radians vs. degrees: 2*pi radians = 360 degrees = 1 full circle.
There are two functions that make up all of standard trig: sine and cosine (usually shortened to sin and cos respectively).
Okay, given a right triangle, take one of the non-right vertices, label it A and label the angle at that vertex x. Note that x is bounded by 0 and pi/2 in radians, and by 0 and 90 in degrees.
Let a denote the length of the side opposite vertex A, let c denote the length of the hypotenuse, and let b denote the length of the remaining side.
Then sin(x) = a/c and cos(x) = b/c.
Another way to look at it is by picturing a unit circle centered at the origin of the coordinate plane. Pick a point X on the circle, and denote by x the angle, measuring counterclockwise, between a ray from the origin through X and a ray from the origin along the positive x-axis.
Then cos(x) is the x coordinate of X and sin(x) is the y coordinate of X.
Note that by Pythagoras' theorem, (cos(x))^2 + (sin(x))^2 = 1 for all x.
Note also that, in radians, cos(pi/2-x) = sin(x), and in degrees, cos(90-x)=sin(x).
Now there are four other basic trig functions, all expressable in terms of sin and cos.
Tangent: tan(x) = sin(x)/cos(x)
Secant: sec(x) = 1/cos(x)
Cosecant: csc(x) = 1/sin(x)
Cotangent: cot(x) = cos(x)/sin(x)
The other four trig functions also show up on the circle.
See picture:
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