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What is the relationship between those trigonometry function e.g sine and cos and also tan curve?
Wiki User
∙ 14y ago
Given that theta is the angle with respect to the positive X axis of a line of length 1, then sin(theta) = Y and cos(theta) is X, with (X,Y) being the point at the end of the line. As theta sweeps from 0 to 360 degrees, or 0 to 2 pi radians, that point draws a circle of radius 1, with center at (0,0).
Since X, Y, and 1 form the sides of a right triangle, where 1 is the hypotenuse, then the pythagorean theorem states that X2 + Y2 = 12. This means that sin2(theta) + cos2(theta) = 1.
Tan(theta) is defined as sin(theta) divided by cos(theta), or Y / X. Since division by zero is a limiting invalidity, then tan(theta) is asymptotic to Y=0, having value of +infinity at theta = 90 or pi / 4, and -infinity at 270 or 3 pi / 4.
Wiki User
∙ 14y ago
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