Trigonometry Sample Questions

11th Standard

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Business Maths

Time : 01:00:00 Hrs
Total Marks : 50
    5 x 1 = 5
  1. The degree measure of \(\frac{\pi}{8}\) is

    (a)

    20o60'

    (b)

    22o30'

    (c)

    20o60'

    (d)

    20o30'

  2. If \(\tan\theta=\frac{1}{\sqrt5}\) and \(\theta\) lies in the first quadrant, then \(\cos\theta\) is

    (a)

    \(\frac{1}{\sqrt6}\)

    (b)

    \(\frac{-1}{\sqrt6}\)

    (c)

    \(\frac{\sqrt5}{\sqrt6}\)

    (d)

    \(\frac{-\sqrt5}{\sqrt6}\)

  3. The value of sin 15o cos 15o is

    (a)

    1

    (b)

    \(\frac{1}{2}\)

    (c)

    \(\frac{\sqrt3}{2}\)

    (d)

    \(\frac{1}{4}\)

  4. The value of sec A sin(270o+A) is

    (a)

    -1

    (b)

    cos2 A

    (c)

    sec2 A

    (d)

    1

  5. If sin A+ cos A=1, then sin 2A is equal to

    (a)

    1

    (b)

    2

    (c)

    0

    (d)

    \(\frac{1}{2}\)

  6. 5 x 2 = 10
  7. Find the principal value of the following
    \(\sin^{-1}\left(\frac{-1}{2}\right)\)

  8. Find the principal value of the following
    cosec-1(2)

  9. Determine the quadrants in which the following degree lie. -140°

  10. Find the value of \(\cos\left(\frac{5\pi}{12}\right)\)

  11. Prove that \(sin^2\left(\frac{\pi}{8}+\frac x2\right)-sin^2\left(\frac{\pi}{8}-\frac x2\right)=\frac{1}{\sqrt2}\sin x.\)

  12. 5 x 3 = 15
  13. Prove that \(\sqrt3\)cosec 20o-sec 20o=4

  14. Prove that  \(2\sin ^{ 2 }{ \frac { \pi }{ 6 } } +\ cosec ^{ 2 }{ \frac { 7\pi }{ 6 } } \cos ^{ 2 }{ \frac { \pi }{ 3 } } =\frac { 3 }{ 2 } \)

  15. Prove that:  \(\sin { \theta } \cos { \theta } \left\{ \sin { \left( \frac { \pi }{ 2 } -\theta \right) } \csc { \theta } +\cos { \left( \frac { \pi }{ 2 } -\theta \right) \sec { \theta } } \right\} =1\)

  16. If \(\alpha\) and \(\beta\) are acute angles such that \(\tan\alpha=\frac{m}{m+1}\) and \(\tan\beta=\frac{1}{2m+1}\), prove that \(\alpha+\beta=\frac{\pi}{4}\)

  17. Show that \(\tan\left(\frac{\pi}{3}+x\right)\tan\left(\frac{\pi}{3}-x\right)=\frac{2\cos2x+1}{2\cos2x-1}\)

  18. 4 x 5 = 20
  19. Prove that  \(\frac { \sin { \left( { 180 }^{ o }+A \right) \cos { \left( { 90 }^{ o }-A \right) \tan { \left( { 270 }^{ o }-A \right) } } } \quad \quad }{ \sec { \left( { 540 }^{ o }-A \right) \cos { \left( { 360 }^{ o }+A \right) \ cosec { \left( { 270 }^{ o }+A \right) } } } } =-\sin { A } \cos ^{ 2 }{ A } \)

  20. If \(\sin { A } =\frac { 3 }{ 5 } \) where\(0<A<\frac { \pi }{ 2 } \)  and  \(\cos { B } =\frac { -12 }{ 13 } \) ,   \(\pi <A<\frac { 3\pi }{ 2 } \) , find the values of the following sin (A - B)

  21. Prove that cos22x-cos26x = sin 4x.sin 8x

  22. Prove that cot x cot 2x - cot 2x cot 3x - cot 3x cot x = 1.

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