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Hyperbolic Functions:

Hyperbolic functions are the exponential function represented in the rational form. There are mainly six types of hyperbolic functions.

sin hx = sin hx

cos hx  = cos hx

tan hx = tan hx

cot hx = cot hx

cosec hx = cosec hx

sec hx  = sec hx

 

Hyperbolic Functions Sample Questions:

Question 1: Find the value of x, if 3sinhx – 2coshx -2 = 0

 

value of x


Answer: (b)

Explanation: 3sinhx – 2coshx -2 = 0

Putting the values of hyperbolic functions

 

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Question 2: For x Question 2 cosh(x)  is equal to:

 

(a) Question 2 a

(b) Question 2 b

(c) Question 2 c

(d) Question 2 d


Answer: (d)

Explanation: Answer 2

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Question 3: cothx is equal to

 

(a) Question 3 a

(b) Question 3 b

(c) Question 3 c

(d) Question 3 d


Answer: (a)

Explanation: cothx =  Explanation 3

 

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Question 4: What is the range for tan hx

 

(a) [1,-1]

(b) R

(c) [0,1]

(d) [-1,1]


Answer: (d)

Explanation: The range of tan hx is (-1,1) and domain is R

 

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Question 5: Find the value of cosh^2x – sinh^2x

 

(a) 2

(b) -1

(c) 0

(d) 1


Answer: (d)

Explanation: cosh2x – sinh2x
we know that cos hx = cos ix and sinhx = i sin ix

 

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Question 6: What is the period of sin hx

 

(a) Question 6 a

(b) 2v b

(c) 0

(d) 2iQuestion 6 d


Answer: (b)

Explanation: The period of sin hx

 

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Question 7: If f(x) = log(3x-5) +2 then f-1(x) is

 

(a) Question 7 a

(b) inverse does not exist

(c) Question 7 c

(d) Question 7 d


Answer: (c)

Explanation: f(x) = log (3x-5)+2
y= log(3x-5)+2

 

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Question 8: What is the domain for y =  coth-1x

 

(a) R

(b) [0,1]

(c) R - [-1,1]

(d) [-1,1]


Answer: (c)

Explanation: The domain for coth^-1x

 

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Question 9: Choose the incorrect option

 

(a) sin ix = i sin hx

(b) cos ix = cos hx 

(c) tan hx = -i tan hx  

(d) None of these


Answer: (d)

Explanation: sin ix = i sin hx   
cos ix = cos hx

 

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Question 10: The value of  Question 10is

 

Question 10.1


Answer: (d)

Explanation: Explanation 10

 

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