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Inverse trigonometric functions

Quiz by BALAJI

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10 questions
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  • Q1
    what is the value of arcsin(-1/2)
    -pi/3
    pi/3
    -pi/6
    pi/6
    30s
  • Q2
    What is the value of $\sin^{-1}(1)$?
    $\frac{\pi}{3}$
    $\frac{\pi}{2}$
    $-\frac{\pi}{2}$
    $\frac{\pi}{4}$
    30s
  • Q3
    What is the derivative of $\tan^{-1}(x)$?
    $\frac{1}{1+x^2}$
    $\frac{1}{\cos^2(x)}$
    $\an(x)$
    $-\frac{1}{1+x^2}$
    30s
  • Q4
    If $\cos^{-1}(x) = alpha$, what is the value of $\sin(alpha)$?
    $1-x^2$
    $x$
    $\sqrt{1-x^2}$
    $\frac{1}{\sqrt{1-x^2}}$
    30s
  • Q5
    What is the principal value of $\sec^{-1}(2)$?
    $\frac{\pi}{2}$
    $\frac{\pi}{6}$
    $\frac{\pi}{4}$
    $\frac{\pi}{3}$
    30s
  • Q6
    If $y = \cos^{-1}(\sin(x))$, for which interval of $x$ is $y$ equal to $x$?
    $[0, \frac{\pi}{2}]$
    $[0, \pi]$
    $(-\frac{\pi}{2}, \frac{\pi}{2})$
    $[\frac{\pi}{2}, \pi]$
    30s
  • Q7
    If $\sin^{-1}(x) + \cos^{-1}(x) = k$, what is the value of $k$?
    $1$
    $\pi$
    $\frac{\pi}{2}$
    $\frac{\pi}{4}$
    30s
  • Q8
    What is $\cos^{-1}(-\frac{\sqrt{2}}{2})$?
    $\frac{3\pi}{4}$
    $\frac{\pi}{3}$
    $\frac{\pi}{4}$
    $\frac{\pi}{2}$
    30s
  • Q9
    What is the range of the function $f(x) = tan^{-1}(x)$?
    $[0, \pi]$
    $(-\pi, \pi)$
    $[0, \frac{\pi}{2})$
    $(-\frac{\pi}{2}, \frac{\pi}{2})$
    30s
  • Q10
    If $\sin^{-1}(x) = y$, what is $\cos(y)$?
    $\sqrt{1-x^2}$
    $x^2 - 1$
    $-\sqrt{1-x^2}$
    $\sqrt{x^2-1}$
    30s

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