. Elements of plane and spherical trigonometry . Fig. 10. 23. Prove that (r cos x)2 -\- {r sin x sin y)2 -\- (r sin x cos ?/)2 = 24. In a right triangle given a = 7 inches and sin i? = f6, c, and tan A. 25. In a right triangle given c = 12inches and sec J. = 3: find a, 6, andcos _B. 26. In a right triangle tan B = f andc = 4 inches : find a, b, and sin .4. 27. In Fig. 9, OP =6 inches andPON = 60°. , O/W, and OiVi?are right angles. Find the lengths ofON, PM, PN, NR, and OR. 28. In Fig. 10, OP = 12 inches, POM= 310 N = NOR = 30°. The anglesOPM, OQP, OMN, OSM, ONR, andOTN are all right angle
. Elements of plane and spherical trigonometry . Fig. 10. 23. Prove that (r cos x)2 -\- {r sin x sin y)2 -\- (r sin x cos ?/)2 = 24. In a right triangle given a = 7 inches and sin i? = f6, c, and tan A. 25. In a right triangle given c = 12inches and sec J. = 3: find a, 6, andcos _B. 26. In a right triangle tan B = f andc = 4 inches : find a, b, and sin .4. 27. In Fig. 9, OP =6 inches andPON = 60°. , O/W, and OiVi?are right angles. Find the lengths ofON, PM, PN, NR, and OR. 28. In Fig. 10, OP = 12 inches, POM= 310 N = NOR = 30°. The anglesOPM, OQP, OMN, OSM, ONR, andOTN are all right angles. Find thelengths of OM, ON, OR, PM, MN, NR,PQ, MS, and NT. 29. In Fig. 11, given OP = 6 inches,POR = NST = 60°, and MRT = 45°.PRMN is a square. Find the lengths ofOR, PR, RT, NT, TS, and OS. Find by the use of the logarithmictables the values of the following ex-pressions : X sin 78° 12 X tan2 36° 12 X tan 17° 9 X cos 39° 14 find. 30. 31. 32. X tan 63^ X cos2 9° m i= A pind X sin3 41° 38 X cot 26°/ ( X cos 83° 6 X tan2 79° 38QI(cot3 31° 16 X sin 81° -=- sin2 41° 36)* 21. Trigonometric Functions of any Angle. In Chapter I. an angle was defined in such a way as to admit ofan unlimited numerical measure; but so far the trigonometricfunctions of an angle have been defined with reference onlyto angles less than 90°. We shall show how these definitionsapply to all angles. Let the angle ACPV Fig. 12, be represented by 0V ACP2 by THE TRIGONOMETKIC FUNCTIONS. 27 Fig. 12. B 0r ACP3 by 05, and ACP± by 0V the angles all being measuredin the positive direction, as in § notation is adopted merelyas a matter of convenience, sothat the subscript of 6 may indi-cate the quadrant to which theangle belongs. If we write 0without a subscript it will meanthat the angle is not limited toany particular quadrant. If theangle is 6V it is an acute angle,ACP1 for example, and from thedefinitions (§ 12)
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