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Inverse Trigonometric Functions - Two Marks Study Materials

12th Standard EM

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Maths

Time : 01:00:00 Hrs
Total Marks : 30
    15 x 2 = 30
  1. Find the principal value of sin-1(2), if it exists.

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

  3. Find the value of
    \(2{ cos }^{ -1 }\left( \frac { 1 }{ 2 } \right) +{ sin }^{ -1 }\left( \frac { 1 }{ 2 } \right) \)

  4. Find the value of sec−1\(\left( -\frac { 2\sqrt { 3 } }{ 3 } \right) \)

  5. Prove that \(\frac{\pi}{2}\le sin^{-1}x+2 cos^{-1} x\le\frac{3\pi}{2}\).

  6. Find the value of 
    i) \(sin\left[ \frac { \pi }{ 3 } -{ sin }^{ 2 }\left( -\frac { 1 }{ 2 } \right) \right] \)

  7. Prove that tan-1 x+tan-1 z=tan-1\(\left[ \frac { x+y+z-xyz }{ 1-xy-yz-zx } \right] \)

  8. Find the value of
    \({ cos }^{ -1 }\left( cos\frac { \pi }{ 7 } cos\frac { \pi }{ 17 } -sin\frac { \pi }{ 17 } sin\frac { \pi }{ 17 } \right) .\)

  9. Find the principal value of
    cot-1 \((\sqrt{3})\)

  10. Simplify
    \({ sec }^{ -1 }\left( sec\left( \frac { 5\pi }{ 3 } \right) \right) \)

  11. Simplify
    sin-1[sin10]

  12. Find the principal value of \({ tan }^{ -1 }\left( \cfrac { -1 }{ \sqrt { 3 } } \right) \)

  13. If \({ cot }^{ -1 }\left( \cfrac { 1 }{ 7 } \right) =\theta \) find the value of cos \(\theta \)

  14. Prove that \({ tan }^{ -1 }\left( \cfrac { 1 }{ 7 } \right) +{ tan }^{ -1 }\left( \cfrac { 1 }{ 13 } \right) ={ tan }^{ -1 }\left( \cfrac { 2 }{ 9 } \right) \)

  15. Evaluate \(sin\left( { cos }^{ -1 }\left( \cfrac { 1 }{ 2 } \right) \right) \)
     

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