We show the tangent in the unit circle. The unit circle is a circle with radius equation.

tan-circle

According to the theorem of intersecting lines, the  ratio of the opposite to the adjacent is equal to the ratio of the tangent to the radius of the circle, which is 1 for the unit circle.

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Because in the unit circle, sine is the opposite and cosine is the adjacent, it follows that:

    equation

This is the plot of the tangent function:

tan

Here are some values of the tangent functions that are worth remembering:

Alpha in degree Alpha in radians Value of tan of alpha
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