at what which of the following sets of values is the tangent function undefined?
at 45 and 135 degrees
at 90 and 270 degrees
at 60 and 120 degrees
at 90 and 180 degrees
The tangent function is undefined at angles where the cosine function equals zero, because the tangent of an angle is defined as the ratio of the sine of the angle to the cosine of the angle.
The cosine function equals zero at 90 degrees and 270 degrees, so the tangent function is undefined at those angles.
Therefore, the correct answer is:
At 90 and 270 degrees.