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Inverse Hyperbolic Functions and Integrals Since the hyperbolic functions can be expressed in terms of exponen- tial functions, it is possible to express the inverse hyperbolic functions in terms of logarithms, as shown in the following table. sinh x = In (x + V + 1), coshx = In (x + VF - 1), -00 1 Use these formulas to express the numbers in Exercises 61-66 in terms of natural logarithms. 61. sinh (-5/12) 62. cosh (5/3) 64. coth" (5/4) 66. csch-(-1/V3) 63. tanh-(-1/2) 65. sech (3/5)

Inverse Hyperbolic Functions and Integrals Since the hyperbolic functions can be expressed in terms of exponen- tial functions, it is possible to express the inverse hyperbolic functions in terms of logarithms, as shown in the following table. sinh x = In (x + V + 1), coshx = In (x + VF - 1), -00 1 Use these formulas to express the numbers in Exercises 61-66 in terms of natural logarithms. 61. sinh (-5/12) 62. cosh (5/3) 64. coth" (5/4) 66. csch-(-1/V3) 63. tanh-(-1/2) 65. sech (3/5)

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter4: Exponential And Logarithmic Functions
Section4.3: Logarithmic Functions
Problem 90E
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Inverse Hyperbolic Functions and Integrals Since the hyperbolic functions can be expressed in terms of exponen- tial functions, it is possible to express the inverse hyperbolic functions in terms of logarithms, as shown in the following table. sinh x = In (x + V + 1), coshx = In (x + VF - 1), -00 <x<00 tanhx 1 1 +x |x| < 1 = (1 + sech-x = In 0 <xs1 Vi + x? |x| cschx = In coth-x = |x| > 1 Use these formulas to express the numbers in Exercises 61-66 in terms of natural logarithms. 61. sinh (-5/12) 62. cosh (5/3) 64. coth" (5/4) 66. csch-(-1/V3) 63. tanh-(-1/2) 65. sech (3/5)
Transcribed Image Text:Inverse Hyperbolic Functions and Integrals Since the hyperbolic functions can be expressed in terms of exponen- tial functions, it is possible to express the inverse hyperbolic functions in terms of logarithms, as shown in the following table. sinh x = In (x + V + 1), coshx = In (x + VF - 1), -00 <x<00 tanhx 1 1 +x |x| < 1 = (1 + sech-x = In 0 <xs1 Vi + x? |x| cschx = In coth-x = |x| > 1 Use these formulas to express the numbers in Exercises 61-66 in terms of natural logarithms. 61. sinh (-5/12) 62. cosh (5/3) 64. coth" (5/4) 66. csch-(-1/V3) 63. tanh-(-1/2) 65. sech (3/5)
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