3.4 Circular Functions

is a circle centered at the origin with radius 1 x2 + y2 = 1 is a circle centered at the origin with radius 1 call it “The Unit Circle” Any point on this circle can be defined in terms of sine & cosine (x, y)  (cos θ, sin θ) (1, 0) Ex 1) For the radian measure , find the value of sine & cosine. (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. (x, y) r y θ x 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) r 7 θ 3

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

cosθ = 0 Reminder: (–, +) (+, +) sinθ = 0 sinθ = 0 (–, –) (+, –) II I sinθ = 0 sinθ = 0 III IV (–, –) (+, –) 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 2nd quadrant. Find the exact value of cos θ if 10 8 Pythag says: x2 + 82 = 102 x2 = 36 x = ±6 –6 x why negative? so…