. A treatise on plane and spherical trigonometry, and its applications to astronomy and geodesy, with numerous examples . and COB by //; then the angleAOC = 0-y. In 00 take any point P*, anddraw PI), PE, perpendicular toOA and OB respectively; drawKH, , perpendicular to PD and 0OA Then the angle EPH = 90* - HEP = BEH= AOB = x. nrOP V 9) Qp or OP = EK OE HP PE = oeor peop bs sin X 0O8Jf — 0088 sin//. ^-a» n OD OK + 1H OK , EH cos (a; — ?/) = — = as r- v • OP or op op_OK OE EH PE ssoeop peop bb COSX coxy + sin//. Notk 1. — The sign in the expression of the sine hi the MMM
. A treatise on plane and spherical trigonometry, and its applications to astronomy and geodesy, with numerous examples . and COB by //; then the angleAOC = 0-y. In 00 take any point P*, anddraw PI), PE, perpendicular toOA and OB respectively; drawKH, , perpendicular to PD and 0OA Then the angle EPH = 90* - HEP = BEH= AOB = x. nrOP V 9) Qp or OP = EK OE HP PE = oeor peop bs sin X 0O8Jf — 0088 sin//. ^-a» n OD OK + 1H OK , EH cos (a; — ?/) = — = as r- v • OP or op op_OK OE EH PE ssoeop peop bb COSX coxy + sin//. Notk 1. — The sign in the expression of the sine hi the MMM as it is in the angle expanded; In the ooeine it i« the opposite * P is taken in the line bounding the engle nnder oonelderatton; \oc. SINE AND COSINE. 53 Note 2. —In this proof the angle x — y is acute; but the proof, like the one givenin Art. 43, applies to angles of any magnitude whatever. For example, Let AOB, measured in the positive direction, = x, and BOC = 2/. Then \ AOC = *-y. Hp—^E In OC take any point P, and draw C-PD, PE, perpendicular to OA and OBproduced: draw EH, EK, perpendicu-lar to DP and AO , angle EPH = EOK = AOB = 360° - x, and POE = 180°-2/.
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Keywords: ., bookcentury1900, bookdecade1900, booksubjecttrigono, bookyear1902
