Inverse Trigonometric Functions Book Back Questions

12th Standard EM

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Maths

Time : 00:45:00 Hrs
Total Marks : 30
    5 x 1 = 5
  1. The value of sin-1 (cos x),0\(\le x\le\pi\) is

    (a)

    \(\pi-x\)

    (b)

    \(x-\frac{\pi}{2}\)

    (c)

    \(\frac{\pi}{2}-x\)

    (d)

    \(\pi-x\)

  2. If cot−1x=\(\frac{2\pi}{5}\) for some x\(\in\)R, the value of tan-1 x is

    (a)

    \(\frac{-\pi}{10}\)

    (b)

    \(\frac{\pi}{5}\)

    (c)

    \(\frac{\pi}{10}\)

    (d)

    \(-\frac{\pi}{5}\)

  3. The domain of the function defined by f(x)=sin−1\(\sqrt{x-1} \) is

    (a)

    [1,2]

    (b)

    [-1,1]

    (c)

    [0,1]

    (d)

    [-1,0]

  4. \({ tan }^{ -1 }\left( \frac { 1 }{ 4 } \right) +{ tan }^{ -1 }\left( \frac { 2 }{ 3 } \right) \)is equal to

    (a)

    \(\frac { 1 }{ 2 } { cos }^{ -1 }\left( \frac { 3 }{ 5 } \right) \)

    (b)

    \(\frac { 1 }{ 2 } { sin }^{ -1 }\left( \frac { 3 }{ 5 } \right) \)

    (c)

    \(\frac { 1 }{ 2 } {tan }^{ -1 }\left( \frac { 3 }{ 5 } \right) \)

    (d)

    \({ tan}^{ -1 }\left( \frac { 1}{ 2 } \right) \)

  5. If the function f(x)sin-1(x2-3), then x belongs to

    (a)

    [-1,1]

    (b)

    [\(\sqrt2\),2]

    (c)

    \(\\ \\ \\ \left[ -2,-\sqrt { 2 } \right] \cup \left[ \sqrt { 2 } ,2 \right] \)

    (d)

    \(\left[ -2,-\sqrt { 2 } \right] \cap \left[ \sqrt { 2 } ,2 \right] \)

  6. 3 x 2 = 6
  7. Find the period and amplitude of
    y=sin 7x

  8. Find the principal value of
    sec-1\((\frac{2}{\sqrt3})\)

  9. Find the value, if it exists. If not, give the reason for non-existence.
    sin-1(cos\(\pi\))

  10. 3 x 3 = 9
  11. For what value of x , the inequality\(\cfrac { \pi }{ 2 } <{ cos }^{ -1 }(3x-1)<\pi \)

  12. Solve sin-1 x> cos-1x

  13. Find the value of
    \(cos\left( { sin }^{ -1 }\left( \frac { 4 }{ 5 } \right) -{ tan }^{ -1 }\left( \frac { 3 }{ 4 } \right) \right) \)

  14. 2 x 5 = 10
  15. Find the principal value of cos−1\(\left( \frac { \sqrt { 3 } }{ 3 } \right) \)

  16. Find the principal value of
    sec−1(−2).

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