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?

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

sec 7.3159

Concept Check Work each problem. Without using a calculator, determine which of the following numbers is closest to sin 115°: -0.9, -0.1, 0, 0.1, or 0.9.

Find the exact value of s in the given interval that has the given circular function value.

[ π , 3π/2] ; sec s = ―2√3/3

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?

Find the approximate value of s, to four decimal places, in the interval [0 , π/2] that makes each statement true.

sec s = 1.0806

Find exact values of the six trigonometric functions of each angle. Rationalize denominators when applicable. See Examples 2, 3, and 5. 300°

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

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 approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement true.

cos s = 0.9250

Use a calculator to evaluate each expression. cos 75°29' cos 14°31' - sin 75°29' sin 14°31'