. A treatise on plane and spherical trigonometry, and its applications to astronomy and geodesy, with numerous examples . sin A = cosB = cos (90°- A) c cos A = sinB = sin (90°-A) c tan A = cotB = cot (90°- A) a cot A == tanB = tan (90°- A) b ? a sec A = cosecB = cosec (90°- A) c ~b cosec A = secB = sec (90°-A) _ ca vers A = covers B = covers (90° — A) = 1 , c covers A = versB = vers (90°—A) =1 c Therefore the sine, tangent, secant, and versed sine of anangle are equal respectively to the cosine, cotangent, cosecant,and coversed sine of the complement of the angle. 16. Representation of the Tri
. A treatise on plane and spherical trigonometry, and its applications to astronomy and geodesy, with numerous examples . sin A = cosB = cos (90°- A) c cos A = sinB = sin (90°-A) c tan A = cotB = cot (90°- A) a cot A == tanB = tan (90°- A) b ? a sec A = cosecB = cosec (90°- A) c ~b cosec A = secB = sec (90°-A) _ ca vers A = covers B = covers (90° — A) = 1 , c covers A = versB = vers (90°—A) =1 c Therefore the sine, tangent, secant, and versed sine of anangle are equal respectively to the cosine, cotangent, cosecant,and coversed sine of the complement of the angle. 16. Representation of the Trigonometric Functions byStraight Lines. — The Trigonometric functions were for-merly defined as being certain straight lines geometricallyconnected with the arc subtending the angle at the centreof a circle of given radius. Thus, let AP be the arc of a circle subtending the angleAOP at the centre. REPRESENTATION OF FUNCTIONS BY LINES. 21 Draw the tangents AT, BT meeting OP prodnced to Tr,and draw PC, PD ± to OA, Then PC was called the sine of the arc AP. oc U cosine a AT a tangent a BT ii cotangent a OT ii secant a OT a cosecant a AC a versed sine a BD ii coversed sine a Since any arc is the measure of the angle at the centrewhich the arc subtends (Art. 5), the above functions of thearc AP are also functions of the angle AOP. It should be noticed that the old functions of the arc abovegiven, when divided by the radius of the circle, become themodern functions of the angle which the arc subtends at thecentre. If, therefore, the radius be taken as unity, the oldfunctions of the arc AP become the modern functions of theangle AOP. Thus, representing the arc AP, or the angle AOP by 6, wehave, when 0 A = OP = 1? 22 PLANE TRIGONOMETRY. ?•-iihr-** and similarly for the other functions. Therefore, in a circle whose radius is unity, the Trigono-metric functions of an arc, or of the angle at the centre meas-ured by that arc, may be defined as follows: The sine is the
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Keywords: ., bookcentury1900, bookdecade1900, booksubjecttrigono, bookyear1902
