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

$31^{\circ}$F

Since March $15$ corresponds to Day $74$, we substitute $x=74$ in the formula: $T(74)=37+21\sin[\frac{2\pi}{365}(x-91)]$ $T(74)=37+21\sin[\frac{2\pi}{365}(74-91)]$ $T(74)=37+21\sin[\frac{2\pi}{365}(-17)]$ $T(74)=37+21\sin[-0.293]$ $T(74)=37+21(-0.289)$ $T(74)=37-6.065$ $T(74)=30.93\approx31^{\circ}$F Therefore, on Day $74$, the temperature is $31^{\circ}$F.