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

question 263

Short Answer

Solve the problem.
-The formula
$$\mathrm { D } = 24 \left[ 1 - \frac { \cos ^ { - 1 } ( \tan \mathrm { i } \tan \theta ) } { \pi } \right]$$
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, $\cos ^ { - 1 }$ (tan i tan $\theta$ ) must be expressed in radians. Approximate the number of hours of daylight in Fargo, North Dakota, (4652'north latitude) for vernal equinox $\left( \mathrm { i } = 0 ^ { \circ } \right)$ . orth