3. Unit Circle

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)?

Consider the equation $\sin \theta$. If $\theta$ is an angle in Quadrant II, what is the value of $\sin \theta$?

Which expression is equivalent to $\cos 120°$?

Write the complex exponential function $e^{i\theta }$ as a sum of its real and imaginary parts:

For which values of $\theta$ is the expression ${\sec }^2\theta \cos \left(2\theta \right)$ defined on the unit circle?

On the unit circle, which of the following points would map onto itself after a reflection across the line $y=-x$?

Given the function $y=3\cdot \sin \left(x\right)$, what is the amplitude of the sinusoidal function?

For the function $f\left(x\right)=\sin \left(x\right)$ on the unit circle, what is its minimum value?

Which of the following expressions has the same value as $\tan (-45°)$?

If the terminal side of an angle measuring $\theta$ radians is in standard position, at what point does it intersect the unit circle?

Which expression is equivalent to $\cos 120°$?

Which of the following steps correctly explains how to find the exact value of $\sin (570°)$ on the unit circle?