1. Modeling the Path of the Sun Using Trigonometry

2. Background information:
Latitude and Longitude of Raleigh, NC: °N, °W Latitude of Arctic Circle: ° Tilt of Earth: 90° – ° = ° Complement of Raleigh’s Latitude: 90° ° = ° Solar Angle at Solar Noon: ° ≤  ≤ ° Hour of Sunlight varies between hrs and hrs with the angle of α = ° Time of Solar Noon: hrs = 12:14:33.5
Spring Equinox
Summer Solstice
Fall Equinox
Winter Solstice
Date
March 20, 2016
June 20, 2016
September 22, 2016
December 21, 2016
Days into Year 80
171
265
355
Sunrise
89°
60°
119°
Solar Noon
54.4°
77.7°
54.2°
30.8°
Sunset
271°
300°
270°
241°
Hours of Sunlight
Tilt of Axis with Sun
0.2°
23.4°
0.0°
–23.4°

3. Modeling the Sun Angle at Solar Noon
Model the solar angle at noon as a sinusoidal function y = A cos (B(x – C)) + D of the number of days into the year using the above table and the graph above as a guide.

4. Modeling the Number of Hours of Daylight
Model the number of hours of daylight as a sinusoidal function y = A cos (B(x – C)) + D of the number of days into the year using the above table and the graph above as a guide.

5. Modeling the Sun Angles from North of Sunrise and Sunset
Model the sun angle from North for sunrise as a sinusoidal function y = A cos (B(x – C)) + D of the number of days into the year using the above table and the graph above as a guide.

6. Modeling the Sun Angle at Solar Noon
Model the solar angle at noon as a sinusoidal function y = A cos (B(x – C)) + D of the number of days into the year using the above table and the graph above as a guide.

7. Sun Chart Path for Raleigh, NC http://solardat. uoregon

8. Polar Sun Chart for Raleigh, NC