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its the tangent of the angle the slope makes with the x-axis
Sine is NOT the y coordinate: it is the sine of the angle made by the x-axis and the radius from a point on the circle. It is the cosine of the angle made with the y-axis.Consider any point, P, on the unit circle with coordinates (x, y). And let Q be the foot of the perpendicular from P to the x-axis. Then y = PQ.Now, in the right angled triangle OPQ, if OP makes an angle theta with the x axis, then sin(theta) = PQ/OP = y/OP and since OP is the radius of a unit circle, OP = 1 so that sin(theta) = y.
It is a 90 degree angle, or a right anlge, plus another 45 degrees. So you can visualize it as a 45 degree angle measured from the negative side of the x axis going toward the positive y axis on the x-y plane.
A line which rotates through an angle of 10 degree with the positive side of the x-axis of the Cartesian plane is called a 10 degree angle.
a coordinate grid