The moon's illumination changes in a periodic way that can be modeled by a trigonometric function. On the night of a full moon, the moon provides about $0.25$ lux of illumination (lux is the SI unit of illuminance). During a new moon, the moon provides $0$ lux of illumination. The period of the lunar cycle is $29.53$ days long. The moon will be full on December $25$, $2015$. Note that December $25$ is $7$ days before January $1$. **Find the formula of the trigonometric function that models the illumination $L$ of the moon $t$ days after January $1$, $2016$. Define the function using radians.** $\qquad L(t) = $ [[☃ expression 1]]