11/25/22 - Sinusoidal Functions, Secant, Cosecant, and Cotangent

Question 1

What is the format of a sinusoidal function?

Answer 1

f(x) = Asin(B(x - h)) + k

A = vertical stretch
k = vertical shift
B = horizontal stretch by 1/B
h = horizontal shift

Question 2

Is cos(x) a sinusoidal function?

Answer 2

Yes, it is sin(x) shifted left by pi/2 units

Question 3

How do you find the amplitude of a sinusoidal function?

Answer 3

In f(x) = Asin(B(x - h)) + k, amplitude = A

Question 4

How do you find the midline of a sinusoidal function?

Answer 4

In f(x) = Asin(B(x - h)) + k, the midline is y = k

Question 5

How do you find the period of a sinusoidal function?

Answer 5

In f(x) = Asin(B(x - h)) + k, the period is 2π/B

Question 6

Find the amplitude, midline, and period of f(x) = 4sin(π/3(x + 1)) - 2

Answer 6

Amplitude: 4
Midline: y = -2 [max: y = 2, min: y = -6]
Period: 2π/(π/3) = 6

Question 7

What is the value of sec(x)?

Answer 7

sec(x) = 1/cos(x)

Question 8

What is the value of csc(x)?

Answer 8

csc(x) = 1/sin(x)

Question 9

What is the value of cot(x)?

Answer 9

cot(x) = cos(x)/sin(x)