. A text book of physics, for the use of students of science and engineering . tieth of a degree,and a second is one-sixtieth of a minute. An angle of 42 degrees,35 minutes, 12 seconds is written 42° 35 12. A radian is the angle subtended at the centre of a circle by an arcequal to the radius of the circle. There are 2?r radians in a complete circle, hence2tt radians = 360 degrees. TV 180 in DYNAMICS CHAP. Let I be the length of arc subtended by an angle, and let r be theradius of the circle, both in the same units ; then angle = l/r radians. Trigonometrical ratios. In Fig. 6 let OB revolve an
. A text book of physics, for the use of students of science and engineering . tieth of a degree,and a second is one-sixtieth of a minute. An angle of 42 degrees,35 minutes, 12 seconds is written 42° 35 12. A radian is the angle subtended at the centre of a circle by an arcequal to the radius of the circle. There are 2?r radians in a complete circle, hence2tt radians = 360 degrees. TV 180 in DYNAMICS CHAP. Let I be the length of arc subtended by an angle, and let r be theradius of the circle, both in the same units ; then angle = l/r radians. Trigonometrical ratios. In Fig. 6 let OB revolve anti-clockwise about O, and let it stop successivelyin positions OPl5 OP2, OP3, OP4; theangles described by OB are said tobe as follows : PxOB, in the first quadrant ,OB, in the second quadrant (greater than 180°), in the third quadrant (greater than 270°); in thefourth quadrant BOD. Drop perpendiculars such as PiMlfrom each position of P on to is always regarded as positive ;OM is positive if on the right andnegative if on the left of O ; PM. FlQ. 6.—Trigonometrical ratios. is positive if above and negative if below AB. Name of ratio. Ratio as written. Value ofratio. Algebraic sign of ratio. 1st quad. 2nd quad. 3rd quad. 1th quad. sine POM sin POM - PMOP + + - — cosine POM cos POM - OMOP + - - + tangent POM - (an POM - PMOM + - + - ecant POM - cosec POM - OPPM + + - - i nt POM sec POM - OP OM + - - + at POM cot POM - OMPM + - + - The values of bhe ratios are aol affected by the length of the liua OP. The following formulae are .riven for reference : 1 1 1 . BecA = - ; cotA = — •>A cos A tan A MATHEMATICAL FORMULAE 11 tan A = - ; cot A = - —- ; cos2A + sin2A = A sin A sin A = cos (90° -A) ; sin A = sin (180° -A). sin (A + B) = sin A cos B + cos A sin B. cos (A + B) =cos A cos B - sin A sin B. sin (A - B) = sin A cos B - cos A sin B. cos (A - B) = cos A cos B + sin A sin B. tan A + tan Btan(A + B) = 1_tanAtanB- y 1 + tan A tan
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