Question

the myrtle beach skywheel has:
middle height: 102 feet
radius: 85 feet
on a previous screen found the height of a person
who started at the bottom then turned 60 degree.
to get the answer you typed
85 sin(60 + 270) + 102 in the calculator.
below type an expression for the height of a person
after starting from the bottom and turning any
number of degrees(x)
(hint: type what you have been typing in the
calculator, but instead of the degrees turned type x
)
attempts: 0

Explanation:

Step1: Analyze the general form of the sine - based height formula

The general form of a sinusoidal function for height \(h\) is \(h = A\sin(B(x - C))+D\). Here, the amplitude \(A\) is the radius of the wheel (\(A = 85\)), the vertical shift \(D\) is the middle height (\(D=102\)).

Step2: Determine the phase - shift

When \(x = 60\), we know the formula \(h=85\sin(60 + 270)+102\). For a general angle \(x\) (in degrees), using the pattern from the given example (where the argument of the sine function is the sum of the angle \(x\) and \(270^{\circ}\)), the formula for the height of a person after turning \(x\) degrees starting from the bottom is \(h = 85\sin(x + 270)+102\).

Answer:

\(85\sin(x + 270)+102\)