Hyperbolic Functions

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If cosec θ = cosh z, then the value of sinh z is

tan θ

cot θ (correct)

sin θ

sec θ

What is the value of tanh(x + y) when cosh x = sec θ and sec y = cosec θ?

tan θ (correct)

tanh θ

coth θ

cot θ

If cosh z = 3, then what is the value of sinh z?

√2

√5 (correct)

2√3

2√2

What is the value of coth x when cosec θ = cosh x?

cot θ (D) Signup and view all the answers

If tanh x = 1/2, then what is the value of cosh x?

2/√3 (A) Signup and view all the answers

If log sec x = y, then the value of y is

2 coth-1 (cosec 2 - 1) (D) Signup and view all the answers

The value of cosh-1 (sec x) is

log(1 + sin x / cos x) (C) Signup and view all the answers

If tanh x = 1/2, then the value of coth x is

3 (C) Signup and view all the answers

The value of sinh-1 (tan x) is

log(sec x + tan x) (D) Signup and view all the answers

If cosech x = 2, then the value of x is

log(2 + √(2^2 - 1)) (A) Signup and view all the answers

If $f(x) = \cosh{x} + \sinh{x}$, then $f(p) = f(x) \cdot f(y)$, what is the value of $p$?

f(x_1) \cdot f(x_2) \cdot... \cdot f(x_n) (C) Signup and view all the answers

What is the value of $\cosh^2{x} - \sinh^2{x}$?

1 (A) Signup and view all the answers

If $\sin{x} \cosh{y} = \cos{\theta}$ and $\cos{x} \sinh{y} = \sin{\theta}$, what is the value of $\sinh^2{y}$?

1 - cos(2x) (D) Signup and view all the answers

What is the value of $\tanh{x} + \tanh{y}$?

1 + \tanh{x} \tanh{y} (D) Signup and view all the answers

What is the value of $\cosh{2x} - 1$?

2 \sinh^2{x} (B) Signup and view all the answers

What is the formula for tan⁻¹(cos θ + i sin θ) when cos θ > 0?

sin⁻¹(sin θ) + i log(sin θ + 1 + sin θ) (A) Signup and view all the answers

If x = log(y + √(y² + 1)), then what is y in terms of x?

sinh x (D) Signup and view all the answers

If cosh⁻¹ x = log(2 + 3), then what is the value of x?

2 (A) Signup and view all the answers

Which of the following is true about inverse hyperbolic functions?

They are many-valued. (D) Signup and view all the answers

What is the formula for sinh⁻¹(cos θ + i sin θ)?

cos⁻¹(sin θ) - i log(sin θ + 1 + sin θ) (A) Signup and view all the answers

What is the value of sin$^{-1}$(cosec $\theta$) in terms of $\theta$?

$\pi/2 + i$ log(cot $\theta$) (B) Signup and view all the answers

What is the real part of cos$^{-1}$(cos $\theta + i$ sin $\theta$)?

$\pi/2$ (B) Signup and view all the answers

What is the value of sin$^{-1}$(sin $\theta - i$ cos $\theta$)?

$\pi - \theta - i$ log(cos $\theta$) (C) Signup and view all the answers

What is the value of cos$^{-1}$(cos $\theta + i$ sin $\theta$) in terms of $\theta$?

$\theta + i$ log(sin $\theta$) (D) Signup and view all the answers

What is the domain of the hyperbolic sine function?

R (A) Signup and view all the answers

If $e^x - e^{-x} = 4$, what is the value of $ ext{sinh} x$?

2 (C) Signup and view all the answers

What is the range of the hyperbolic cosine function?

[1, ∞) (C) Signup and view all the answers

If $ ext{cosh} x = 2$, what is the value of $ ext{sinh} x$?

√3 (B) Signup and view all the answers

What is the value of $ ext{tanh} 0$?

0 (D) Signup and view all the answers

What is the relationship between sin(x) and sinh(ix)?

sin(x) = -i sinh(ix) (B) Signup and view all the answers