In trigonometry, the signs of trigonometric functions (sine, cosine, tangent) in different quadrants can help us determine their values for a given angle. To find out which statement about 214° is correct, let's analyze each trigonometric function:
A. sin 214° < 0:
Since the sine function is negative in the third and fourth quadrants, where sine is the y-coordinate of the point on the unit circle, sin 214° is indeed less than 0 because 214° falls in the third quadrant where y-coordinates are negative.
B. tan 214° < 0:
The tangent function is negative in the second and fourth quadrants. Since 214° is in the third quadrant, where tangent is negative because the x-coordinate is positive and y-coordinate is negative, tan 214° is less than 0.
C. cos 214° > 0:
For cosine, it is positive in the first and fourth quadrants. However, since 214° is in the third quadrant where x-coordinates are negative, cos 214° is less than 0.
Therefore, the correct statement about 214° is:
B. tan 214° < 0
