. A treatise on plane and spherical trigonometry, and its applications to astronomy and geodesy, with numerous examples . OM - OM 36 PLANE TRIGONOMETRY. 33. To prove sin (— A) = — sin A, cos (— A) = cos A, tan (— A) = — tan A. B Let OP and OP be the positions ofthe radius for any equal angles AOPand AOP measured from the initialline AO in opposite directions. Thenif the angle AOP be denoted by A, thenumerically equal angle AOP will bedenoted by —A (Art. 4). The triangles POM and POM are geometrically PM .\ sin(-A) = sinAOP = ^^ = PM OP OP sin A, cos ( — A) = cos AOP: OM OM A = = cos A,
. A treatise on plane and spherical trigonometry, and its applications to astronomy and geodesy, with numerous examples . OM - OM 36 PLANE TRIGONOMETRY. 33. To prove sin (— A) = — sin A, cos (— A) = cos A, tan (— A) = — tan A. B Let OP and OP be the positions ofthe radius for any equal angles AOPand AOP measured from the initialline AO in opposite directions. Thenif the angle AOP be denoted by A, thenumerically equal angle AOP will bedenoted by —A (Art. 4). The triangles POM and POM are geometrically PM .\ sin(-A) = sinAOP = ^^ = PM OP OP sin A, cos ( — A) = cos AOP: OM OM A = = cos A, OP OP tan (-A) = tan AOP: PM PM OM OM = — tan A. 34. To prove sin (270° + A) = sin (270° - A) =and cos (270° + A) = - cos (270°- A) B = sin A. Let the angle AOP = A; then theangles AOQ and AOE, measured inthe positive direction, =(270°— A) Aand (270°+A) respectively. The triangles POM, QON, and EOLare geometrically equal. — cos A,
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Keywords: ., bookcentury1900, bookdecade1900, booksubjecttrigono, bookyear1902
