Unit circle and radians Knowledge-Based Practice

Questions

1. 1.

   In which quadrant does the terminal ray of an angle measuring 4 radians in standard position lie?

   • A) Quadrant I
   • B) Quadrant II
   • C) Quadrant III
   • D) Quadrant IV
2. 2.

   An angle measuring $-\frac{19\pi}{6}$ radians is in standard position. Which of the following angles in the interval $[0, 2\pi)$ is coterminal with this angle?

   • A) $\frac{\pi}{6}$
   • B) $\frac{\pi}{3}$
   • C) $\frac{5\pi}{6}$
   • D) $\frac{7\pi}{6}$
3. 3.

   A terminal ray in standard position intersects the unit circle at a point with an $x$-coordinate of $-\frac{\sqrt{3}}{2}$. If the $y$-coordinate of this point is negative, what is the measure of the angle $\theta$ in radians, where $0 \le \theta < 2\pi$?

   • A) $\frac{2\pi}{3}$
   • B) $\frac{5\pi}{6}$
   • C) $\frac{7\pi}{6}$
   • D) $\frac{11\pi}{6}$
4. 4.

   A point $P(x, y)$ lies in the second quadrant on the unit circle. If $y = \frac{\sqrt{5}}{3}$, what is the value of $x$?

   • A) $\frac{2}{3}$
   • B) $-\frac{2}{3}$
   • C) $-\frac{4}{9}$
   • D) $-\frac{\sqrt{14}}{3}$
5. 5.

   What are the coordinates of the point on the unit circle that corresponds to the angle $\theta = \frac{5\pi}{6}$ radians in standard position?

   • A) $\left(-\frac{\sqrt{3}}{2}, \frac{1}{2}\right)$
   • B) $\left(-\frac{1}{2}, \frac{\sqrt{3}}{2}\right)$
   • C) $\left(\frac{\sqrt{3}}{2}, -\frac{1}{2}\right)$
   • D) $\left(-\frac{\sqrt{3}}{2}, -\frac{1}{2}\right)$

Answers and step-by-step solutions appear after you finish the test.