3. Unit Circle

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

Find all values of θ, if θ is in the interval [0°, 360°) and has the given function value. See Example 6. cos θ = √3 2

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?

Without using a calculator, decide whether each function value is positive or negative. (Hint: Consider the radian measures of the quadrantal angles, and remember that π ≈ 3.14.)

cos 6

In Exercises 8–13, find the exact value of each expression. Do not use a calculator. sec 22𝜋 3

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?

The radius of the unit circle intersects the circle at the point where the angle is $\frac{\pi }{4}$ radians. What is the approximate value of $y$ at this point?