Final answer:
The tangent of the angle 7π/2 is undefined because it corresponds to the positive y-axis of the unit circle, where the cosine is zero, and division by zero is not defined. The tangent function at this angle is undefined, making the correct answer (d) Undefined.
Step-by-step explanation:
The tangent of the angle 7π/2 is undefined because it corresponds to the positive y-axis of the unit circle, where the cosine is zero, and division by zero is not defined.
The student has asked to evaluate the trigonometric function of the quadrant angle tan(7π/2). The tangent function, which is the ratio of the sine to the cosine of an angle, is undefined at quadrant angles where the cosine of the angle is 0. This is because division by zero is undefined in mathematics. The angle 7π/2 corresponds to the positive y-axis on the unit circle, where the cosine of an angle is, indeed, 0. Therefore, the tangent function at this angle is undefined, making the correct answer (d) Undefined.