3. Unit Circle

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

In Exercises 25–30, use an identity to find the value of each expression. Do not use a calculator. sec² 23° - tan² 23°

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?

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?

Find the exact values of (a) sin s, (b) cos s, and (c) tan s for each real number s. See Example 1.

s = ―π

Find one solution for each equation. Assume all angles involved are acute angles. See Example 3. sin(2θ + 10°) = cos(3θ - 20°)

Find a calculator approximation to four decimal places for each circular function value.

sec 7.3159

For each value of s, use a calculator to find sin s and cos s, and then use the results to decide in which quadrant an angle of s radians lies.

s = 65