4.3 Highlights

Question 1

Provide the:
endpoint coordinates and
θ°

For these radians:
0 
π/6
π/4
π/3 
π/2 
π
2π

Answer 1

0 radians: (1,0): 0°
π/6 radians: (√3/2, 1/2): 30°
π/4 radians: (√2/2, √2/2): 45°
π/3 radians: (1/2, √3/2): 60°
π/2 radians: (0,1): 90°
π radians: (-1,0): 180°
2π radians: (1,0): 360°

Question 2

If no units are given for an angle, assume the units are

Answer 2

radians

Question 3

The cosine of θ, denoted __ θ, is the ___ coordinate of the endpoint of the radius of the unit circle corresponding to θ

Answer 3

cos

first

Question 4

The sine of θ, denoted __ θ, is the ___ coordinate of the endpoint of the radius of the unit circle corresponding to θ

Answer 4

sin

second

Question 5

The endpoint of the radius of the unit circle corresponding to θ has coordinates (__ θ, __ θ)

Answer 5

(cos, sin)

Question 6

Degrees to

cosθ and sinθ

Answer 6

degrees: cos θ: sin θ
0° : 1 : 0 
30° : √3/2 : 1/2 
45°: √2/2 : √2/2
60°: 1/2 : √3/2
90°: 0 : 1
180°: -1 : 0 
360°: 1 : 0

Question 7

The quadrant in which a radius lies determines whether the corresponding cos or sin are

Answer 7

positive or negative

Question 8

Relationship between cosine and sine

Answer 8

(cosθ)^2 + (sinθ)^2 = 1

Question 9

Where will sin be if:

−1 ≤ cos θ ≤ 1

Answer 9

− 1 ≤ sin θ ≤ 1

Question 10

The domain of both cos and sin are the ___

Answer 10

set of real numbers

Question 11

The range of both cos and sin is in the interval

Answer 11

[-1,1]