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

In Exercises 5–18, the unit circle has been divided into twelve equal arcs, corresponding to t-values of 0, 𝜋, 𝜋, 𝜋, 2𝜋, 5𝜋, 𝜋, 7𝜋, 4𝜋, 3𝜋, 5𝜋, 11𝜋, and 2𝜋. 6 3 2 3 6 6 3 2 3 6 Use the (x,y) coordinates in the figure to find the value of each trigonometric function at the indicated real number, t, or state that the expression is undefined.

tan 0

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

Find the exact values of s in the given interval that satisfy the given condition.

[0 , 2π) ; cos² s = 1/2

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?

Find each exact function value. See Example 2.

sin (-4π/3)

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.