The tangent of an angle is positive for angles whose terminal arm is in Quadrant III since sine and cosine are both negative. Since sine is negative and cosine is positive for angles with their terminal arm in Quadrant IV, the tangent is also negative.
The tangent of an angle in trigonometry is the ratio of the lengths of the adjacent side to the opposing side. In order for the value of the cosine function to not be 0, it is the ratio of the sine and cosine functions of an acute angle.
The length of the opposite side (O) divided by the length of the adjacent side (A) determines the angle's tangent in any right triangle (A). It is denoted by the single letter "tan" in a formula. As long as the acute angle's measure is known, we may use tangent to determine the length of the side of a right triangle that is next to it.
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