3. Unit Circle

Use the formula ω = θ/t to find the value of the missing variable.

θ = 2π/9 radian , ω = 5π/27 radian per min

Use the formula ω = θ/t to find the value of the missing variable.

ω = 0.91 radian per min, t = 8.1 min

Identify the quadrant that the given angle is located in.

$\frac{7\pi}{4}$ radians

Identify the quadrant that the given angle is located in.

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

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.

$\frac{6\pi}{5}$ radians

Test whether the point is on the unit circle by plugging it into the equation, $x^2+y^2=1$.

$\left(\frac{-\sqrt2}{2},\frac{-\sqrt2}{2}\right)$

Use the formula ω = θ/t to find the value of the missing variable.

ω = 2π/3 radians per sec, t = 3 sec

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/2

Find the exact values of (a) sin s, (b) cos s, and (c) tan s for each real number s. See Example 1.

s = 2π

Use the formula ω = θ/t to find the value of the missing variable.

θ = 3π/4 radians, t = 8 sec

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

Use the formula ω = θ/t to find the value of the missing variable.

θ = 3.871 radians, t = 21.47 sec

Find each exact function value. See Example 2. sin 7π/6