Question

In two or more complete sentences, use your knowledge of the unit circle to describe why the following trigonometric equation is true: tan(-20°) = -tan(20°).

a) The unit circle does not apply to this equation.
b) The angles are complementary.
c) Tangent is an odd function.
d) The angles have opposite signs.

Answer 1

The equation tan(-20°) = -tan(20°) is true because tangent is an odd function, displaying symmetry about the origin on the unit circle, which is a property that applies to all angles.

Step-by-step explanation:

The trigonometric equation tan(-20°) = -tan(20°) is true because the tangent function is an odd function. This means that tangent has the property of odd symmetry about the origin on the unit circle. Therefore, if you have an angle {\displaystyle \theta } and its negative counterpart {\displaystyle -\theta }, tan(-\theta) = -tan(\theta). This property is not unique to 20 degrees; it applies to all angles and is due to the inherent symmetry of the sine and cosine functions that compose the tangent function, where tan(\theta) = sin(\theta)/cos(\theta).