3. Unit Circle

If the period of a trigonometric function is $T$, how many complete cycles of the function occur in a horizontal length of $L$?

On the unit circle, if the terminal point is at $(x,y)$, how many radius lengths is it to the right of the circle's vertical diameter?

Given the sequence defined by $a_n=\cos \left(n\pi \right)$, which of the following lists the first five terms of the sequence?

On the unit circle, for $0<\theta <\pi$, when is $tan\left(\theta \right)$ undefined?

Given two unit vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ on the unit circle, what is the angle $\theta$ between them if $\overrightarrow{a}$ = $\left(1,0\right)$ and $\overrightarrow{b}$ = $\left(0,1\right)$? Express your answer using one significant figure.

Which of the following statements is true about the measure of an inscribed angle that intercepts an arc on the $unitcircle$?

Given the parametric equation $r\left(t\right)=\left(\cos \right(t),\sin (t),t)$, where does the helix lie?

Figure 10.1 should remind you of trigonometric functions you've seen before. Which of the following functions is most directly represented by the coordinates of a point on the unit circle at an angle $\theta$ from the positive x-axis?

Given the polar equation $r^2=\sin \left(2\theta \right)$, which of the following best describes the shape of its graph on the unit circle?

On the unit circle, which trigonometric functions are undefined when $x=0$?

Which of the following represents the polar equation $r=(\tan 2\pi )(\csc \pi )$ as a rectangular equation?

Given a point on the unit circle corresponding to an angle $\theta$ measured from the positive x-axis, what is the x-coordinate of the point (x, y)?

The angles that share the same tangent value as $\tan (45°)$ have terminal sides in which quadrant(s)?