3. 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?

Find each exact function value. See Example 2.

sin (-4π/3)

(Modeling) Grade Resistance Solve each problem. See Example 3. A 3000-lb car traveling uphill has a grade resistance of 150 lb. Find the angle of the grade to the nearest tenth of a degree.

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

sin s = 0.9918

Use a calculator to determine whether each statement is true or false. A true statement may lead to results that differ in the last decimal place due to rounding error. sin 10° + sin 10° = sin 20°

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:

(Modeling) Grade Resistance Solve each problem. See Example 3. A car traveling on a -3° downhill grade has a grade resistance of -145 lb. Determine the weight of the car to the nearest hundred pounds.

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

cot s = 0.5022