Final answer:
The terminal point on the unit circle determined by −13π/4 radians is (-√2/2, √2/2), corresponding to the coordinate in the second quadrant for the angle 3π/4.
Step-by-step explanation:
The student has asked to find the terminal point on the unit circle for the angle −13π/4 radians. To find this, we first need to reduce the angle to a coterminal angle between 0 and 2π radians. Since the full rotation in radians is 2π (which equals 8π/4), we can add this to −13π/4 until we get an equivalent positive angle that falls within the desired range.
−13π/4 + 2(8π/4) = −13π/4 + 16π/4 = 3π/4
This reduced angle corresponds to a point in the second quadrant on the unit circle where both sine and cosine are negative. The terminal point for 3π/4 on the unit circle is (√2/2, √2/2), but since it is in the second quadrant, the x-coordinate (cosine) should be negative. Therefore, the terminal point is (√2/2, √2/2).