Solve the problem.
-The temperature in Fairbanks is approximated by
$$T ( x ) = 37 \sin \left[ \frac { 2 \pi } { 365 } ( x - 101 ) \right] + 25$$
where $\mathrm { T } ( \mathrm { x } )$ is the temperature on day $x$, with $x = 1$ corresponding to Jan. 1 and $x = 365$ corresponding to Dec. 31. Estimate the temperature on day 49 .
A) $- 29 ^ { \circ }$
B) $45 ^ { \circ }$
C) $- 25 ^ { \circ }$
D) $- 4 ^ { \circ }$

Question

Quizplus · Accepted Answer

To estimate the temperature on day 49, substitute $x = 49$ into the given equation: $T(49) = 37 \sin\left[\frac{2\pi}{365}(49 - 101)\right] + 25$. Simplifying inside the sine function and calculating the sine value, then multiplying by 37 and adding 25 gives a result close to $-4^\circ$, which corresponds to choice D.

Solve the Problem T(x)=37sin⁡[2π365(x−101)]+25T ( x ) = 37 \sin \left[ \frac { 2 \pi } { 365 } ( x - 101 ) \right] + 25T(x)=37sin[3652π​(x−101)]+25

Solve the Problem $T ( x ) = 37 \sin \left[ \frac { 2 \pi } { 365 } ( x - 101 ) \right] + 25$