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Tangent and Cotangent Functions

In figure 4.2a below, a unit circle is drawn. We know that the vertical axis passing through the center is the sine axis and the horizontal axis passing through the center is the cosine axis.

 
figure 4.2a

The vertical axis that is tangent to the circle at the point A is called the tangent-axis. The horizontal axis that is tangent to the circle is called the cotangent axis. To find the tangent of the angle AOB, simply locate the points of intersection of the side OB with these axes. The distances of these points from the origins of the axes are called the tangent and cotangent of the angle AOB.