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 90 and 180 degrees at 60 and 120 degrees

Answer 1

The tangent function is undefined when the cosine of the angle is zero, since the tangent function is defined as the ratio of sine to cosine (\( \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} \)). Therefore, we need to find angles where \(\cos(\theta) = 0\).

The angles where cosine is zero in degrees are:

• \(90^\circ\)
• \(270^\circ\)

From the given options, \(90^\circ\) and \(270^\circ\) are the angles at which the tangent function is undefined.

Therefore, the correct set of values is at 90 and 270 degrees.