tion one of the vertices is usually the pole and the sides b and c are colatitudes. The distance between points B and C can be computed knowing the latitude and longitude of each point Angle A is difference in longitude using the cosine rule. Quadrant ambiguity in the cos-1 is not a problem because the shortest distance between the points is less than 180o The bearing between the points is computed from the sine rule once the distance is known.09/28/2009 12.215 Modern Naviation L04 13 Azimuth or Bearing calculation In the azimuth or bearing calculation quadrant ambiguity is a problem since the sin-1 will return two possible angles that yield the same value for sine. To resolve the quadrant ambiguity: rewrite the cosine rule for sides since all sides are now known in the form: cos B cos b - cos c cos a/sin c sin a Then use the two-argument tan-1 to compute the angle and correct quadrant. Note: That the aziumuth to travel back to point is not simply 180oforward azimuth. To stay on a great circle path the azimuth or bearing of travel has to change along the parth.09/28/2009 12.215 Modern Naviation L04 14 Homework Homework 1 is available on the 12.215 web page 12.215_HW01 Due Wednesday October 7 2009 Solutions to the homework can be submitted on paper or emailed to tahmit.edu as a PDF or Word document.09/28/2009 12.215 Modern Naviation L04 15 Summary In this class we –Reviewed plane trigonometry –Introduced concepts in Spherical Trigonometry Distance measures Azimuths and bearings –Developed the basic formulas: Cosine rule Sine rule –Discuss some ways these formulas are used09/28/2009 12.215 Modern Naviation L04 16c C j J 0q Q7x Xd Eampk L1 rS8 yY fF mM2 sT 9z gG nN 3u UaB hI -o O5v Vc Cj J pQ6 wXd Damp kK0 rR 7yY eF lL 2sS 9z ZfG m N3t Ua Ah Ho O4 vVb B iI pP 6wW cD jK 0qR 7x XeE ampl L1s S8y Zf Fm M2 tT9 A gH nN4 uU bB iI -oP 5v WcC jJ q Q6x Xd Eampk K1 rR8 yYf F lM2 sT 9zZ gG nN 3uU aA hH -o O5v
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