Question Continuation
The finger hole changes by 45 degrees.
Define a function, f, that gives the height of the finger hole above the ground (in inches) in terms of the angle of rotation (measured in radians) it has swept out from the 12 o'clock position.
Answer:
f(θ) = r(1 + cos(θ)) for 0 ≤ θ ≤ π/4
Step-by-step explanation:
Given
Let represent radius
r = 4 inches
Considering that she starts tracking the location when the finger hole is at the 12 o'clock; this means that the angle measurement at this point is 0°.
Let θ represent the angle
At 12 o'clock mark
θ = 0
When the finger hole changes by 45 degrees
θ = 45°
Convert 45° to radians
θ = 45° * π/180
θ = π/4
So, angle θ is such that θ∈[0, π/4]
This can be represented as
0 ≤ θ ≤ π/4
Calculating the measure of f(θ) in polar coordinates
When θ = 0, f(θ) = r (i.e. the current position of the bowl)
When θ = π/2, f(θ) = rcosθ
This is so because f(θ), being the function of the height is a measure of the radius* cos(θ)
Taking measurement of f(θ) from 0 to π/2
f(θ) = r + rcosθ
f(θ) = r(1 + cos(θ))
So, f(θ) = r(1 + cos(θ)) for 0 ≤ θ ≤ π/4
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