Elements of geometry and trigonometry . 222 PLANE XVI. The square of the sinecf an arc, together ivith thesquare of the cosine, is equalto the square of the radius ; sothat in general terms we havesin^A + cos^A^Rl This property results im-mediately from the right-an-gled triangle CMP, in whichMP-+CP^=CM. It follows that w^hen thesine of an arc is given, its co-,sine may be found, and re-ciprocally, by means of the formulas cos A = ri= V (R^—sin^A), and sin A = =b V (R^—cos^A).The sign of these formulas is +, or-^, because the same sineMP answers to the two arcs AM, AM, whose cos
Elements of geometry and trigonometry . 222 PLANE XVI. The square of the sinecf an arc, together ivith thesquare of the cosine, is equalto the square of the radius ; sothat in general terms we havesin^A + cos^A^Rl This property results im-mediately from the right-an-gled triangle CMP, in whichMP-+CP^=CM. It follows that w^hen thesine of an arc is given, its co-,sine may be found, and re-ciprocally, by means of the formulas cos A = ri= V (R^—sin^A), and sin A = =b V (R^—cos^A).The sign of these formulas is +, or-^, because the same sineMP answers to the two arcs AM, AM, whose cosines CP, CP,are equal and have contrary signs ; and the same cosine CPanswers to the two arcs AM, AN, whose sines MP, PN, arealso equal, and have contrary signs. Thus, for example, having found sin 30°=iR, we mav de-duce from it cos 30°, or sin 60° = V (R^—iR^) = V fR^r^iR ^f 3. XVIÎ. The sine and cosine of an arc A being given, it is re-quired to find the tangent, secant, cotangent, and cosecant of thesame arc. The triangles CPM, CAT, CDS, being sim
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