Little-known fact The shortest day of the year occurs on the winter solstice (near December 21) and the longest day of the year occurs on the summer solstice (near June 21). However, the latest sunrise and the earliest sunset do not occur on the winter solstice, and the earliest sunrise and the latest sunset do not occur on the summer solstice. At latitude 40° north, the latest sunrise occurs on January 4 at 7:25 A.M. (14 days after the solstice), and the earliest sunset occurs on December 7 at 4:37 P.M. (14 days before the solstice). Similarly, the earliest sunrise occurs on July 2 at 4:30 A.M. (14 days after the solstice) and the latest sunset occurs on June 7 at 7:32 P.M. (14 days before the solstice). Using sine functions, devise a function S(t) that gives the time of sunrise t days after January 1 and a function S(t) that gives the time of sunset t days after January 1. Assume s and S are measured in minutes and that s = 0 and S = 0 correspond to 4:00 A.M. Graph the functions. Then graph the length of the day function
Want to see the full answer?
Check out a sample textbook solutionChapter 1 Solutions
Calculus: Single Variable, Early Transcendentals and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition) (Briggs, Cochran, Gillett & Schulz, Calculus Series)
- Holes are to be drilled in the length of angle iron as shown in Figure 38-1. What is thedistance between two consecutive holes?arrow_forwardDetermine the size of x to the nearest hundredth degree.arrow_forwardCalculate the declination and right ascension of the sun when it is at longitude 90° (summer solstice) and longitude 45°. By symmetry, find the declination at longitudes 270° and 315°.arrow_forward
- How many radians has the hand of a clock turned from 12:00 to 4:00?arrow_forwardAn angle's terminal ray sweeps out 162 degrees, and then an additional 1.5 radians. This angle sweeps out what percent of a full rotation? What is the radian measure of this angle? What is the degree measure of this angle?arrow_forwardA wheel is rotating 240 times per minute. Through how many degrees does a point on the edge of the wheel move in 1/2 seconds?arrow_forward
- Two wheels are rotating in such a way that the rotation of the smaller wheel causes the larger wheel to rotate. The radius of the smaller wheel is 8.8 centimeters and the radius of the larger wheel is 16.9 centimeters. Through how many degrees (to the nearest hundredth of a degree) will the larger wheel rotate if the smaller one rotates 180°?arrow_forwardWhat is the period and starting point (d) of this graptharrow_forward
- Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781305652224Author:Charles P. McKeague, Mark D. TurnerPublisher:Cengage Learning