Plane And Spherical Trigonometry
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To quickly assess the difficulty of the text, read a short excerpt:
5. cosh7^^ = -l. 15^ sech(- 2:)= secha:.
6. sinh2w7r = 0. 16, csch(- a:)= - cscha;.
7. cosh2n7r = l. 17. cosh^a: — sinh^a; = 1.
8. tanh = 0. 18. sech^a; -[- tanh^a; = 1.
19. csch^a; — coth2a:= — 1.
20. cosh (a: + ?/) = cosh x cosh 2/ -|- sinh x sinh ^.
21. sinh 2 a; = 2 sinh a; cosh x, 22. cosh 2 a; = cosh^ x + sinh^ a:.
23. sinh X — sinh «/ = 2 cosh — — ^ sinh "~ ^ ^ 2 2 a? -4— t/ X ■"" 2/ 24. cosh X + cosh y = 2 cosh — — ^ cosh — — ^ • •^ 2 2 25. cosh X — cosh V = 2 sinh — — -^ sinh — — -^ • ...^ 2 2 113. The notation for inverse hyperbolic functions is the same as for inverse circular functions (Art. 84. p. 111).
If f/ = sinh X, then, X = sinh~i«/.
But by (6), p. 169, y = fl^El!.
Solving this equation for a:, we have a: = log(y + V/ + l). (1) .-. sinli-iy = log(y + Vy + 1).
172 PLANE TRIGONOMETRY In like manner, oosh"^^ = log (jy + Vy^ — 1) ; (2) tanh-V = |logf±^; (3) 2s 1 — V y coth-i«/ = tanh-i - = \ log ^^ ; (4) V 'I V — \ y ^ y sech"^ v = cosh~i - = log ^ ; (5) y y K-l • 1 -1 1 1 1 + Vl+ ?/2 csch ■^v = sinn ^-=log ^-' y y EXERCISE XXX Prove the following relations : , 2 X 1.
What to read after Plane And Spherical Trigonometry?
You can find similar books in the "Read Also" column, or choose other free books by Conant, L. L to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
5. cosh7^^ = -l. 15^ sech(- 2:)= secha:.
6. sinh2w7r = 0. 16, csch(- a:)= - cscha;.
7. cosh2n7r = l. 17. cosh^a: — sinh^a; = 1.
8. tanh = 0. 18. sech^a; -[- tanh^a; = 1.
19. csch^a; — coth2a:= — 1.
20. cosh (a: + ?/) = cosh x cosh 2/ -|- sinh x sinh ^.
21. sinh 2 a; = 2 sinh a; cosh x, 22. cosh 2 a; = cosh^ x + sinh^ a:.
23. sinh X — sinh «/ = 2 cosh — — ^ sinh "~ ^ ^ 2 2 a? -4— t/ X ■"" 2/ 24. cosh X + cosh y = 2 cosh — — ^ cosh — — ^ • •^ 2 2 25. cosh X — cosh V = 2 sinh — — -^ sinh — — -^ • ...^ 2 2 113. The notation for inverse hyperbolic functions is the same as for inverse circular functions (Art. 84. p. 111).
If f/ = sinh X, then, X = sinh~i«/.
But by (6), p. 169, y = fl^El!.
Solving this equation for a:, we have a: = log(y + V/ + l). (1) .-. sinli-iy = log(y + Vy + 1).
172 PLANE TRIGONOMETRY In like manner, oosh"^^ = log (jy + Vy^ — 1) ; (2) tanh-V = |logf±^; (3) 2s 1 — V y coth-i«/ = tanh-i - = \ log ^^ ; (4) V 'I V — \ y ^ y sech"^ v = cosh~i - = log ^ ; (5) y y K-l • 1 -1 1 1 1 + Vl+ ?/2 csch ■^v = sinn ^-=log ^-' y y EXERCISE XXX Prove the following relations : , 2 X 1.
What to read after Plane And Spherical Trigonometry?
You can find similar books in the "Read Also" column, or choose other free books by Conant, L. L to read onlineMoreLess
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