Modeling the Path of the Sun Using Trigonometry

Background information: Latitude and Longitude of Raleigh, NC: 35.7806°N, 78.6389°W Latitude of Arctic Circle: 66.5628° Tilt of Earth: 90° – 66.5628° = 23.4372° Complement of Raleigh’s Latitude: 90° - 35.7806° = 54.2194° Solar Angle at Solar Noon: 30.7822° ≤  ≤ 77.6566° Hour of Sunlight varies between 9.57254 hrs and 14.42746 hrs with the angle of α =18.20597° Time of Solar Noon: 12.242593 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 12.15417 14.58639 12.12917 9.73222 Tilt of Axis with Sun 0.2° 23.4° 0.0° –23.4° http://www.timeanddate.com/sun/usa/raleigh

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.

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.

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.

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.

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

Polar Sun Chart for Raleigh, NC