Trigonometry for Beginners As Far As the Solution of Triangles
Trigonometry for Beginners As Far As the Solution of Triangles
J B John Bascombe Lock
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-. Sin^— = sinr900 -^^=cos^. [Art. 94. ] EXAIUPLES. XLIV. Find A from each of the six following equations, A being an angle of a triangle. 1. Cos^ = J. 2. Cos^=-J. 3. BmA = i. 4. Tan^=-l. 5. J2 8mA=:h 6. TanA^-JS. Prove the following statements, A, Bj G being the angles of a triangle. 7. Sin(^ + B + C) = 0. 8. Cos(^+J5 + C)=-l. 9. Binj(^ + B + 0) = 1. 10. Cosi{A + B + C)=0, 11, tan(^ + J5)=-tanC. 12. Cot J (J5+. C) = tanp. 13. Cos(^+^)=-cosC. 14. Cos(^ + 5-C)=-cos2a 15. Tan A-cotB=cos G . Sec A... . Cosec B, - - sin ^ - sin P, G . A-B 16. -^ — : : — ^ = tan — . Tan — ^r— . "■ 6m^4-sm5 2 2 sin 3 B -sin 3(7 _^ 3jl ^^' cos3C-cos3^~*^'' 2 • 104 TRIGONOMETRY, 154. II. To prove a = ^JJosjC^ 4- c cos^S^ From A, any one of the angular points, draw AD per- pendicular to BO, or to £C produced if necessary. There will be three cases. Fig. I. When both B and are acute angles ; Fig. Ii. When one of them (^) is obtuse ; Fig. Iii. When one of them (B) is a right angle. Then, CD rig. I.
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