The tangent function is undefined at angles where the cosine function equals zero, because tangent is defined as the ratio of the sine to the cosine (tan(θ) = sin(θ) / cos(θ)). The cosine function is zero at the following angles:
- 90 degrees
- 270 degrees
Therefore, the tangent function is undefined at 90 degrees and 270 degrees.
So, the correct response is: at 90 and 270 degrees.