3. Unit Circle

On the unit circle centered at point $O$, which of the following best describes a central angle whose intercepted arc has a length equal to $1$ unit?

On the unit circle, in which quadrant are both $\cos$ and $\cot$ negative?

What is the value of $\tan \frac{\pi }{3}$ on the unit circle?

Which of the following explains why $\cos (60°)$ equals $\sin (30°)$ using the unit circle?

Which of the following expressions is equivalent to $\sin (22°)$?

Given the function $y=3\cdot \sin \left(2x\right)$, what are its amplitude and period?

On the unit circle, if point A is at $(1,0)$ and point D is at $(0,1)$, what is the measure in radians of the arc from A to D (arc AD)?

Given $x=\sin \frac{\pi }{2}$ and $y=\cos \frac{\pi }{2}$, which of the following is correct for $x$ and $y$ where $0\le \theta \le \pi$?

Which of the following situations can be modeled with a periodic function?

Which expression is equivalent to $\sin \frac{7\pi }{6}$?

On the unit circle, what is the radian measure of the arc that subtends a central angle of $90°$?

On the unit circle, what relationship do the ratios $\frac{\sin x}{1}$ and $\frac{\cos y}{1}$ share for any real values of $x$ and $y$?

Find the sine, cosine, and tangent of each angle using the unit circle.

$\theta=-1.18$ rad, $\left(\frac{5}{13},-\frac{12}{13}\right)$

Find the sine, cosine, and tangent of each angle using the unit circle.

$\theta=225\degree,\left(-\frac{\sqrt2}{2},-\frac{\sqrt2}{2}\right)$