3. Unit Circle

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°)

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

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\))$

In Exercises 1–4, a point P(x, y) is shown on the unit circle corresponding to a real number t. Find the values of the trigonometric functions at t.

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