Solve the Problem $\mathrm { T } ( \mathrm { x } ) = 40 \sin \left[ \frac { 2 \pi } { 365 } ( \mathrm { x } - 102 ) \right] + 46$

Multiple Choice

Solve the problem.
-The temperature in Verlander is modeled by $\mathrm { T } ( \mathrm { x } ) = 40 \sin \left[ \frac { 2 \pi } { 365 } ( \mathrm { x } - 102 ) \right] + 46$ where $\mathrm { T } ( \mathrm { x } )$ is the temperature in degrees Fahrenheit on day $x$ , with $x = 1$ representing January 1 and $x = 365$ representing December 31. Find the temperature on May 20 .

A) $83 ^ { \circ } \mathrm { F }$
B) $64 { } ^ { \circ } \mathrm { F }$
C) $72 ^ { \circ } \mathrm { F }$
D) $70 ^ { \circ } \mathrm { F }$