1. The functions sinh, cosh, tanh are defined by Joos sn 0/2 e e cosh(ar) 2 e2 -ez sinh(a) 2 loosh sinh sinh(r) Cosh(r) e tanh(r) e e- are often referred to as hyperbolic trig functions (the figure above gives some sense why). Pronunciation tips: cosh rhymes with gosh, sinh with pinch, and tanh with ranch. The other hyperbolic trig functions are sech (r) = conh(# » C$ch (#) = inh(@} » Coth(x) = ianh ° (a) Find some identities for hyperbolic trig functions, showing justification (hint: compare to common identities for trig functions) e coth(z)da (b) Evaluate sinh(r) cosh(a) dæ (c) Evaluate (d) Evaluate cosh(r)dr (e) (Optional) Inverses of the hyperbolic trig functions are defined on appropriate domains, and may be expressed in terms of logarithms, for example arcosh(r) n (r+ Vx2 =1) ;x >1 In( x+ Vx2+1);-oo< < 00 arsinh(r) 1 In artanh(r) Use substitutions with hyperbolic trig functions (and a corresponding identity from part (a)) to evaluate -dr and V2+1
1. The functions sinh, cosh, tanh are defined by Joos sn 0/2 e e cosh(ar) 2 e2 -ez sinh(a) 2 loosh sinh sinh(r) Cosh(r) e tanh(r) e e- are often referred to as hyperbolic trig functions (the figure above gives some sense why). Pronunciation tips: cosh rhymes with gosh, sinh with pinch, and tanh with ranch. The other hyperbolic trig functions are sech (r) = conh(# » C$ch (#) = inh(@} » Coth(x) = ianh ° (a) Find some identities for hyperbolic trig functions, showing justification (hint: compare to common identities for trig functions) e coth(z)da (b) Evaluate sinh(r) cosh(a) dæ (c) Evaluate (d) Evaluate cosh(r)dr (e) (Optional) Inverses of the hyperbolic trig functions are defined on appropriate domains, and may be expressed in terms of logarithms, for example arcosh(r) n (r+ Vx2 =1) ;x >1 In( x+ Vx2+1);-oo< < 00 arsinh(r) 1 In artanh(r) Use substitutions with hyperbolic trig functions (and a corresponding identity from part (a)) to evaluate -dr and V2+1
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 67E
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