Final answer:
The student's question has a misunderstanding, as the value tan(theta) = -20/21 does not correspond to theta = 270°, where cos(theta) = 0 and sin(theta) = -1, which would make tan(theta) undefined.
Step-by-step explanation:
The student's question involves finding the exact value of the indicated trigonometric function for theta = 270° where tan(theta) = -20/21. When theta is 270°, this corresponds to a position on the unit circle where the coordinate is at (0, -1), which is straight down on the y-axis. At this angle, the sine function, sin(theta), has a value of -1 and the cosine function, cos(theta), is 0. Since tan(theta) is the ratio of sine over cosine, we cannot use it directly because the cosine of 270° is 0 and division by zero is undefined. However, since the student has provided tan(theta) for a different angle where it has the value -20/21, we need to clarify that tan(theta) does not relate to the angle of 270° directly as that would not be possible.