Chapter 4 - Graphs of the Circular Functions - Section 4.1 Graphs of the Sine and Cosine Functions - 4.1 Exercises - Page 152: 57c

$57^{\circ}$F

For Day $200$, we substitute $x=200$ in the formula: $T(200)=37+21\sin[\frac{2\pi}{365}(x-91)]$ $T(200)=37+21\sin[\frac{2\pi}{365}(200-91)]$ $T(200)=37+21\sin[\frac{2\pi}{365}(109)]$ $T(200)=37+21\sin[1.876]$ $T(200)=37+21(0.954)$ $T(200)=37+20.03$ $T(200)=57.03\approx57^{\circ}$F Therefore, on Day $200$, the temperature is $57^{\circ}$F.