3. Unit Circle

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

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

In Exercises 25–32, the unit circle has been divided into eight equal arcs, corresponding to t-values of 0, 𝜋, 𝜋, 3𝜋, 𝜋, 5𝜋, 3𝜋, 7𝜋, and 2𝜋. 4 2 4 4 2 4 a. Use the (x,y) coordinates in the figure to find the value of the trigonometric function. b. Use periodic properties and your answer from part (a) to find the value of the same trigonometric function at the indicated real number.

cos 9𝜋/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?