1. 3.4 Circular Functions

2. 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)

3. 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

4. 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

5. 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

6. 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:
x = 102
x2 = 36
x = ±6 –6 x
why negative?
so…