3. Unit Circle

Express each angular speed in radians per second. 6 revolutions per second

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

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 = 6π cm, r = 2 cm, ω = π/4 radian per sec

Find exact values of the six trigonometric functions for each angle A.

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\))$

Find the approximate value of s, to four decimal places, in the interval [0, π/2] that makes each statement true.

sin s = 0.4924

Use the formula v = r ω to find the value of the missing variable.

v = 9 m per sec , r = 5 m

Give the exact value of each expression. See Example 5. sin 30°

Identify the quadrant that the given angle is located in.

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

Identify the quadrant that the given angle is located in.

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

In Exercises 31–38, find a cofunction with the same value as the given expression. tan 𝜋 9

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

[0, 2π) ; sin s = -√3/ 2

Use the formula v = r ω to find the value of the missing variable.

r = 12 m , ω = 2π/3 radians per sec

Use the formula v = r ω to find the value of the missing variable.

v = 12 m per sec, ω = 3π/2 radians per sec