The Unit Circle and Trignomoetric Functions

Question

Let C be the circle of radius 6 centered at the origin O(0, 0). Let P be the point (5, 0). Let Q be the point in the first quadrant on C such that ∠POQ measures 30◦ . Let R be the point in the second quadrant such that ∠QOR measures 105◦ .

(a) Sketch C and the points O, P, Q, and R.

(b) Find the exact coordinates of Q and R.

(c) Find the length of the arc of C subtended by ∠POR.

Answer 1

(b). Q = (6cos30°, 6sin30°) = (3√3, 3)

R = (6cos135°, 6sin135°) = (-3√2, 3√2)

(c). ∠POR = 135° = 3π/4

Arc length = (radius)(measure of central angle in radians) = 9π/2

Answer 2

(b)

For both points use

x = r sin θ

y = r cos θ

(c)

RQ is 75/360 of the Circumference