Trigonometry for Beginners As Far As the Solution of Triangles

Cover 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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