Final answer:
Cosecant (θ) is undefined when the sine of angle θ is zero. On the unit circle, sine is zero at 0° and 180°, thus csc(θ) is undefined at these angles.
Step-by-step explanation:
The cosecant function, csc(θ), is the reciprocal of the sine function. It is defined as csc(θ) = 1/sin(θ). Since the sine of an angle is the y-coordinate of the corresponding point on the unit circle, cosecant is undefined wherever the sine is zero, which occurs at 0° (or 0 radians) and 180° (or π radians). These are the angles where the points on the unit circle fall on the x-axis, thus having y-coordinate values of zero. Therefore, csc(θ) is undefined at 0° and 180°, corresponding to the angles where the unit circle intersects the x-axis.