Unit circle and radians Knowledge-Based Download PDF

Questions

1. 1.

   A central angle $\theta$ in standard position on the unit circle intercepts an arc of length $\frac{5\pi}{4}$ units along the circumference in the counterclockwise direction from $(1, 0)$. What is the value of $\sin \theta + \cos \theta$?

   • A) $-1$
   • B) $0$
   • C) $-\sqrt{2}$
   • D) $\sqrt{2}$
2. 2.

   In standard position on the unit circle, in which quadrant does the terminal side of an angle measuring $-\frac{11\pi}{4}$ radians lie?

   • A) Quadrant II
   • B) Quadrant III
   • C) Quadrant IV
   • D) Quadrant I
3. 3.

   On the unit circle, the terminal point of an arc of length $\theta$ radians measured counterclockwise from $(1, 0)$ lies in Quadrant II with a $y$-coordinate of $\frac{\sqrt{21}}{5}$. What is the value of $\cos \theta$?

   • A) $-\frac{2}{5}$
   • B) $\frac{2}{5}$
   • C) $-\frac{4}{25}$
   • D) $-\frac{\sqrt{5}}{5}$
4. 4.

   A central angle $\theta$ in standard position terminates in the second quadrant and intersects the unit circle at a point with an $x$-coordinate of $-\frac{1}{2}$. What is the radian measure of $\theta$ on the interval $[0, 2\pi)$?

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

   What are the coordinates of the point on the unit circle corresponding to an angle of $\frac{7\pi}{6}$ 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) $\left(-\frac{\sqrt{3}}{2}, \frac{1}{2}\right)$