Final answer:
The exact value of tan(3π/4) is found by considering its placement in the second quadrant of the unit circle, where tangent values are negative. Since tan(π/4) is 1, and the angle 3π/4 is in the second quadrant, tan(3π/4) equals -1.
Step-by-step explanation:
The student asked to find the exact value of tan(3π/4). This angle corresponds to 135 degrees when converted from radians to degrees, which places it in the second quadrant on the unit circle. In the second quadrant, the sine component is positive while the cosine component is negative, therefore the tangent, which is the ratio of sine to cosine, will be negative. Since tan(π/4) equals 1, and the angle 3π/4 is an extension into the second quadrant, we must take into account the change in sign due to the cosine being negative there. Thus, tan(3π/4) = -1, making the answer C) -1.