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

question 25

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 $\left( \mathrm { i } = 23.5 ^ { \circ } \right)$ .

---

Definitions:

Pooled Standard Deviation

A method of estimating the standard deviation across two or more sample sets by pooling their variances under the assumption that the population variances are equal.

Sample Means

The average values derived from multiple sample sets drawn from a population, important in understanding the population's overall mean.

Control Limits

The boundaries in control charts that indicate the limits of expected variations in a stable process.

Pooled Standard Deviation

A method for estimating standard deviation across two or more groups that assumes equal variances.