Chapter 6.3: Unit Circle & Trigonometric Functions of Any Angle

Question 1

What is the equation for the Pythagorean Identity?

Answer 1

sin²θ + cos²θ = 1

Question 2

What defines the coordinates of a point on the unit circle?

Answer 2

(x, y) where cosθ = x and sinθ = y

Question 3

What is the value of sin s when s is an angle measured in radians?

Answer 3

sin s = sin θ

Question 4

What is the circumference of the unit circle?

Answer 4

C = 2π

Question 5

What is the result of W(2π) on the unit circle?

Answer 5

(1, 0)

Question 6

For s = π, what is the terminal point W(π) on the unit circle?

Answer 6

(-1, 0)

Question 7

What happens to the terminal point when wrapping a string of length -5π around the unit circle?

Answer 7

W(-5π) = (-1, 0)

Question 8

What are the six trigonometric functions evaluated at s when W(s) = (-1, 0)?

Answer 8

sin s = 0, cos s = -1, tan s = 0, csc s = undefined, sec s = -1, cot s = undefined

Question 9

What is the periodicity of sine and cosine functions?

Answer 9

sinθ = sin(θ + n360) and cosθ = cos(θ + n360) for any integer n

Question 10

True or False: The sine and cosine functions are periodic with a period of 360 degrees.

Answer 10

True

Question 11

Fill in the blank: The value of a trigonometric function at the real number s is equal to its value at ______.

Answer 11

s radians

Question 12

What is the relationship between the terminal sides of coterminal angles?

Answer 12

They pass through the same point (x, y)

Question 13

What is the wrapping function denoted as?

Answer 13

W(s) = (x, y)

Question 14

What is the relationship between the radius of the unit circle and its circumference?

Answer 14

The radius is 1, thus C = 2πr = 2π

Question 15

What is the significance of the point (1, 0) on the unit circle?

Answer 15

It is the initial point for measuring arc length s