30 Questions
If cosec θ = cosh z, then the value of sinh z is
cot θ
What is the value of tanh(x + y) when cosh x = sec θ and sec y = cosec θ?
tan θ
If cosh z = 3, then what is the value of sinh z?
√5
What is the value of coth x when cosec θ = cosh x?
cot θ
If tanh x = 1/2, then what is the value of cosh x?
2/√3
If log sec x = y, then the value of y is
2 coth-1 (cosec 2 - 1)
The value of cosh-1 (sec x) is
log(1 + sin x / cos x)
If tanh x = 1/2, then the value of coth x is
3
The value of sinh-1 (tan x) is
log(sec x + tan x)
If cosech x = 2, then the value of x is
log(2 + √(2^2 - 1))
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)
What is the value of $\cosh^2{x} - \sinh^2{x}$?
1
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)
What is the value of $\tanh{x} + \tanh{y}$?
1 + \tanh{x} \tanh{y}
What is the value of $\cosh{2x} - 1$?
2 \sinh^2{x}
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)
If x = log(y + √(y² + 1)), then what is y in terms of x?
sinh x
If cosh⁻¹ x = log(2 + 3), then what is the value of x?
2
Which of the following is true about inverse hyperbolic functions?
They are many-valued.
What is the formula for sinh⁻¹(cos θ + i sin θ)?
cos⁻¹(sin θ) - i log(sin θ + 1 + sin θ)
What is the value of sin$^{-1}$(cosec $\theta$) in terms of $\theta$?
$\pi/2 + i$ log(cot $\theta$)
What is the real part of cos$^{-1}$(cos $\theta + i$ sin $\theta$)?
$\pi/2$
What is the value of sin$^{-1}$(sin $\theta - i$ cos $\theta$)?
$\pi - \theta - i$ log(cos $\theta$)
What is the value of cos$^{-1}$(cos $\theta + i$ sin $\theta$) in terms of $\theta$?
$\theta + i$ log(sin $\theta$)
What is the domain of the hyperbolic sine function?
R
If $e^x - e^{-x} = 4$, what is the value of $ ext{sinh} x$?
2
What is the range of the hyperbolic cosine function?
[1, ∞)
If $ ext{cosh} x = 2$, what is the value of $ ext{sinh} x$?
√3
What is the value of $ ext{tanh} 0$?
0
What is the relationship between sin(x) and sinh(ix)?
sin(x) = -i sinh(ix)
Solve problems involving trigonometric functions and logarithms. Practice your skills in calculating values of logarithms and trigonometric identities.
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