Question

which statement about 214° is correct?
a. cos 214° > 0
b. sin 214° < 0
c. tan 214° < 0

Explanation:

Step1: Determine the quadrant of \(214^{\circ}\)

Since \(180^{\circ}<214^{\circ}<270^{\circ}\), \(214^{\circ}\) is in the third quadrant.

Step2: Analyze the sign of trigonometric functions in the third quadrant

In the third quadrant, \(\sin\theta<0\), \(\cos\theta<0\), and \(\tan\theta=\frac{\sin\theta}{\cos\theta}>0\) (because a negative divided by a negative is positive).

Answer:

B. \(\sin214^{\circ}<0\)