# Useful Formulae

sinC 14 SPHERICALTRIGONOMETRY formulae for heaven and earth A spherical trianglehas internal angles whose sum is between180 and 540. Its sides are arcs of great circles whose centres all lie at the spheres centre. Any two points on a sphere can define a great circle, and any three alesser circle. Any circle on a sphere,greater or lesser, defines two poles. The sides of a spherical triangle can be thought of as angles. The six relevant quantities are shown opposite and obey Law of Sines Law of Cosines cosa cosb cosc sinb sinc cosA cosA cosB cosC sinB sinCcosa Law of Tangents Spherical trigonometry is used in navigation. For example,using degreeslongitudeand latitude,a ship sails from Qto R a 90lat.R b 90lat.Q C long.Qlong.R Cis known as thepolar angle.The initial and final courses are given by Aand B and the length of the journey byc. Use the following equations to solve for B,Aand c tan BA cos ba sec ba cot C tan BA sin ba csc ba cot C tan c tan ba sin BA csc BA tan AB tan AB tan a b tan a b sinc sinb sinB sina sinA 15