Question

Use the table to answer the question.

Complete the Table for f(θ) for the Given Values of θ
θ
f(θ)

0
π4

π2

3π4

π

Use the table of values to graph the f(θ)=4sin(2θ)
and find the amplitude, midline, and period.

(1 point)
Responses

amplitude=2, midline: y=4
, period =π2

amplitude=2, midline: y is equal to 4 , period is equal to pi over 2

amplitude=4, midline: y=0
, period =π

amplitude=4, midline: y is equal to 0 , period is equal to pi

amplitude=2, midline: y=0
, period =π4

amplitude=2, midline: y is equal to 0 , period is equal to pi over 4

amplitude=4, midline: y=2
, period =π4

Answer 1

First fill the table for f(θ)=4 sin(2θ):

- θ = 0: f = 4 sin(0) = 0
- θ = π/4: f = 4 sin(π/2) = 4
- θ = π/2: f = 4 sin(π) = 0
- θ = 3π/4: f = 4 sin(3π/2) = −4
- θ = π: f = 4 sin(2π) = 0

So the values are 0, 4, 0, −4, 0.

Amplitude = |4| = 4. Midline = y = 0 (no vertical shift). Period = 2π / 2 = π.

(The matching response: amplitude=4, midline: y=0, period = π.)