Solve the Problem $$\mathrm { D } = 24 \left[ 1 - \frac { \cos ^ { - 1 } ( \tan i \tan \theta ) } { \pi } \right]$$

Short Answer

Solve the problem.
-The formula
$$\mathrm { D } = 24 \left[ 1 - \frac { \cos ^ { - 1 } ( \tan i \tan \theta ) } { \pi } \right]$$
can be used to approximate the number of hours of daylight when the declination of the sun is $i ^ { \circ }$ at a location $\theta ^ { \circ }$ latitude for any date between the vernal equinox and autumnal equinox. To use this formula, $\cos ^ { - 1 } \left( \tan ^ { i } \tan \theta \right.$ ) must be expressed in radians. Approximate the number of hours of daylight in Flagstaff, Arizona, ( $35 ^ { \circ } 13 ^ { \prime }$ north latitude) for summer solstice $\left( \mathrm { i } = 23.5 ^ { \circ } \right)$ .