Graph the Given Function Over a Two-Period Interval $\mathrm{F}^{\circ}$ ) in London Can Be Modeled Using the Trigonometric Function

Essay

graph the given function over a two-period interval. Identify asymptotes when applicable.
-The average monthly low temperature (in $\mathrm{F}^{\circ}$ ) in London can be modeled using the trigonometric function defined by $f(x)=10 \sin \left[\frac{\pi}{6}(x-4.2)\right]+46$ , where $x$ is the month and $x=1$ corresponds to January.
(a) Graph $f$ over the interval $1 \leq x \leq 25$ .
(b) Determine the amplitude, period, phase shift, and vertical translation of $f$ .
(c) What is the average monthly low temperature for the month of October?
(d) Find the maximum and minimum average monthly low temperatures and the months when they occur.
(e) What would be an approximation for the average yearly low temperature in London? How is this related to the vertical translation of the sine function in the formula for $f$ ?