3.4 Circular Functions

x 2 + y 2 = 1 is a circle centered at the origin with radius 1 call it “The Unit Circle” (1, 0) Ex 1) For the radian measure, find the value of sine & cosine. Any point on this circle can be defined in terms of sine & cosine (x, y)  (cos θ, sin θ) (0, 1)

We can draw a “reference” triangle by tracing the x-value first & then the y-value to get to a point. Use Pythagorean Theorem to find hypotenuse. Ex 2) The terminal side of an angle θ in standard position passes through (3, 7). Draw reference triangle & find exact value of cos θ and sin θ. (3, 7) 3 7 (x, y) x y r θ θ r

Ex 3) Find the exact values of cos θ and sin θ for θ in standard position with the given point on its terminal side. –1 θ r

Reminder: I II III IV (+, +)(–, +) (–, –) (+, –) sinθ = 0 cosθ = 0 Ex 4) State whether each value is positive, negative, or zero. a) cos 75°b) sin (–100°)c) positive negative zero

Ex 5) An angle θ is in standard position with its terminal side in the 2 nd quadrant. Find the exact value of cos θ if – why negative? Pythag says: x = 10 2 x 2 = 36 x = ± 6 so… x

Homework #304 Pg 145 #1–49 odd