Plane And Spherical Trigonometry
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In our eReader you can find the full English version of the book. Read Plane And Spherical Trigonometry Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book 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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