Question

In 1–2 sentences, describe how to determine the sign for tanθ in each quadrant of the coordinate plane.

Answer 1

To determine the sign of \( \tan \theta \) in each quadrant of the coordinate plane, recall that \( \tan \theta = \frac{\sin \theta}{\cos \theta} \): in the first quadrant (0 to 90 degrees), both sine and cosine are positive, so \( \tan \theta \) is positive; in the second quadrant (90 to 180 degrees), sine is positive and cosine is negative, making \( \tan \theta \) negative; in the third quadrant (180 to 270 degrees), both sine and cosine are negative, so \( \tan \theta \) is positive; and in the fourth quadrant (270 to 360 degrees), sine is negative while cosine is positive, resulting in \( \tan \theta \) being negative.