Circular FunctionsDate: 01/27/2001 at 13:36:39 From: Sheena Subject: Circular Functions How do you define circular functions? Can you give me an example, so I can do them? Date: 01/27/2001 at 14:09:41 From: Doctor Robert Subject: Re: Circular Functions Draw a unit circle: a circle with radius 1 with its center at the origin, that is, the point (0,0). Now imagine a point on that circle moving around in a counterclockwise direction. If you draw a ray from the origin to that point, it makes an angle with the positive horizontal axis. That point on the circle has coordinates. If we define the first coordinate to be the cosine of the angle, and the second coordinate to be the sine of the angle, we have defined a circular function. If the angle is zero degrees, the point on the circle has coordinates (1,0) so that cos(0) = 1 and sin(0) = 0. Now move the point on the circle so that the ray from the origin makes an angle of 45 degrees. You find using Pythagoras' theorem that the coordinates of that point are (root2/2, root2/2) or (.707, .707) roughly. If you consider the angle to be the independent variable, then for the cosine function, the dependent variable takes on the values of the x-coordiante of the point on the circle. Starting at an angle of zero, the value of the cosine function starts at 1 and then decreases to zero (when the angle is 90 degrees) and decreases to -1 (when the angle is 180 degrees). The cosine function is a circular function when defined in this manner. - Doctor Robert, The Math Forum http://mathforum.org/dr.math/ |
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