Question

I'm thinking of an angle in the third quadrant. We will call this angle o. It is measured in degrees. Which of the following statements could never be true?

A) sin(0) = cos(0)
B) tan(0) < 0
C) cos (0) = cos(-0)
D) csc(0) < 0

Answer 1

In the third quadrant, the angle o would have a measurement between 180 degrees and 270 degrees. Using the unit circle or trigonometric identities, we can determine which statements could never be true:
A) sin(0) = cos(0) is true only when the angle is 45 degrees or pi/4 radians, and is not true for any angle in the third quadrant. Therefore, this statement could never be true.
B) tan(0) < 0 is true only for angles between 90 degrees and 180 degrees or between 3pi/2 radians and 2pi radians. Therefore, this statement could never be true in the third quadrant.
C) cos(0) = cos(-0) is always true, regardless of the quadrant in which the angle lies. Therefore, this statement could be true for an angle in the third quadrant.
D) csc(0) < 0 is undefined since csc(0) involves dividing by zero. Therefore, this statement does not make sense and could never be true.




Therefore, the statement that could never be true is:
A) sin(0) = cos(0).