Answer
On June 20th, there will be about 14 hours of daylight.
Work Step by Step
$h = \frac{35}{3}+\frac{7}{3}sin~\frac{2\pi~x}{365}$
We can find $x$ when $h=14$:
$h = \frac{35}{3}+\frac{7}{3}sin~\frac{2\pi~x}{365}$
$3h = 35+7sin~\frac{2\pi~x}{365}$
$sin~\frac{2\pi~x}{365} = \frac{3h-35}{7}$
$sin~\frac{2\pi~x}{365} = \frac{(3)(14)-35}{7}$
$sin~\frac{2\pi~x}{365} = 1$
$\frac{2\pi~x}{365} = arcsin(1)$
$\frac{2\pi~x}{365} = \frac{\pi}{2}$
$x = \frac{365}{4}$
$x = 91~days$
We can find the date that is 91 days after March 21st:
March 31st: 10 days
April 30th: 30 days + 10 days = 40 days
May 31st: 31 days + 40 days = 71 days
June 20th: 20 days + 71 days = 91 days
On June 20th, there will be about 14 hours of daylight.
