Hyperbolic Trig Functions

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Last updated 3:22 PM on 5/27/26
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21 Terms

1
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cosh and sinh = 1 identity

cosh²x-sinh²x=1

2
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tanh and sech = 1 identity

tanh²x+sech²x=1

3
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coth and csch = 1 identity

coth²x-csch²x=1

4
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sinhx

(e^x - e^-x)/2

5
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coshx

(e^x+e^-x)/2

6
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tanhx

(sinh(x))/(coshx)

7
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cothx

(coshx)/sinhx (x/=0)

8
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cschx

1/sinhx (x/=0)

9
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sechx

1/coshx

10
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sinh(x+-y)

sinhxcoshy+-coshxsinhy

11
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cosh(x+-y)

coshxcoshy+-sinhxsinhy

12
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sinh²x

(-1 +cosh(2x))/2

13
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sinh²x

(1 +cosh(2x))/2

14
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sinh(2x)

2sinh(x)cosh(x)

15
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cosh(2x)

cosh²x+sinh²x

16
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sinh^-1x

ln(x+(x²+1)^1/2

17
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cosh^-1x

ln(x+(x²-1)^1/2

18
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tanh^-1x

19
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coth^-1x

20
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sech^-1x

ln((1+(1-x²)^1/2)x

21
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csch^-1x

ln(1/x + ((1+x²)^1/2)/|x|