The moon's distance from Earth varies in a periodic way that can be modeled by a trigonometric function. When the moon is at its perigee (closest point to Earth), it's about $363{,}000 \text{ km}$ away. When it's at its apogee (farthest point from Earth), it's about $406{,}000\text{ km}$ away. The moon's apogees occur $27.3$ days apart. The moon will reach its apogee on January $2$, $2016$. **Find the formula of the trigonometric function that models the distance $D$ between Earth and the moon $t$ days after January $1$, $2016$. Define the function using radians.** $\qquad D(t) = $ [[☃ expression 1]]