#### Answer

The temperature on June 15 is $58.3^{\circ}F$

#### Work Step by Step

June 15 is day 166, so we can use $x = 166$ in the equation:
$T(x)=37~sin[\frac{2\pi}{365}~(x−101)]+25$
$T(166)=37~sin[\frac{2\pi}{365}~(166−101)]+25$
$T(166)=37~sin[1.119]+25$
$T(166)=(37)(0.900)+25$
$T(166) = 58.3^{\circ}F$
The temperature on June 15 is $58.3^{\circ}F$