3. Unit Circle

Determine whether each statement is true or false. If false, tell why. csc 22° ≤ csc 68°

Write each function in terms of its cofunction. Assume all angles involved are acute angles. See Example 2. cos(θ + 20°)

The formula ω = θ/t can be rewritten as θ = ωt. Substituting ωt for θ converts s = rθ to s = rωt. Use the formula s = rωt to find the value of the missing variable.

s = 3π/4 km, r = 2 km, t = 4 sec

Determine whether each statement is true or false. See Example 4. cos 28° < sin 28° (Hint: sin 28° = cos 62°)

Find one solution for each equation. Assume all angles involved are acute angles. See Example 3. tan α = cot(α + 10°)

Find a polar equation for the curve represented by the given Cartesian equation $x^2+y^2=2$.

Find one solution for each equation. Assume all angles involved are acute angles. See Example 3. cos(2θ + 50°) = sin(2θ - 20°)

Find each exact function value. See Example 2.

csc 11π/6

Identify the quadrant that the given angle is located in.

$\(\frac{2\pi}{3}\)$ radians

Identify the quadrant that the given angle is located in.

$\(\frac{\pi}{7}\)$ radians

On the unit circle, what is the length of the radius?

Each figure shows an angle θ in standard position with its terminal side intersecting the unit circle. Evaluate the six circular function values of θ.

The propeller of a 90-horsepower outboard motor at full throttle rotates at exactly 5000 revolutions per min. Find the angular speed of the propeller in radians per second.

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

Find the angular speed ω for each of the following.

a wind turbine with blades turning at a rate of 15 revolutions per minute