Final answer:
Option A and D: The angle θ for which sin θ equals cos θ can only fall in Quadrant I of the Cartesian plane, where both sine and cosine values are positive and equal at 45°.
Step-by-step explanation:
If sin θ equals cos θ, the angle θ must either be in Quadrant I or Quadrant IV. In Quadrant I, both sine and cosine values are positive, and when θ is 45°, sin θ equals cos θ since both are √2/2. In Quadrant IV, sine values are negative and cosine values are positive, but θ cannot terminate here while maintaining sin θ equal to cos θ since the magnitudes would differ. Therefore, for sin θ to equal cos θ, the angle θ may only terminate in Quadrant I.
When sin(theta) = cos(theta), it means that the angle theta is in the first or fourth quadrant. In Quadrant I, both sine and cosine are positive, so they can be equal. In Quadrant IV, both sine and cosine are negative, so they can also be equal. Therefore, the angle theta can terminate in Quadrant I or Quadrant IV.