Log inSign up
AP Precalculus · Question of the Day

AP Precalculus Question of the Day

A fresh daily question to build accuracy, reinforce recall, and turn practice into a steady habit.
Friday, November 6, 2026

Let θ\theta be an angle such that cos⁡θ=−22\cos\theta = -\frac{\sqrt{2}}{2} and sin⁡θ=22\sin\theta = \frac{\sqrt{2}}{2}. What is a possible value for θ\theta in radians?

Keep practicing AP Precalculus

Question of the Day

Answer today's AP Precalculus question, reveal the full explanation, then keep the streak going with a new question every day.

Let θ\theta be an angle such that cos⁡θ=−22\cos\theta = -\frac{\sqrt{2}}{2} and sin⁡θ=22\sin\theta = \frac{\sqrt{2}}{2}. What is a possible value for θ\theta in radians?

  1. π4\frac{\pi}{4}
  2. 3π4\frac{3\pi}{4} (correct answer)
  3. 5π4\frac{5\pi}{4}
  4. 7π4\frac{7\pi}{4}

Explanation: The condition cos⁡θ<0\cos\theta < 0 (negative x-coordinate) and sin⁡θ>0\sin\theta > 0 (positive y-coordinate) places the angle in Quadrant II. The reference angle for which cosine and sine have a magnitude of 22\frac{\sqrt{2}}{2} is π4\frac{\pi}{4}. The angle in Quadrant II with this reference angle is π−π4=3π4\pi - \frac{\pi}{4} = \frac{3\pi}{4}.