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Trigonometry Two Marks Questions

11th Standard

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Maths

Time : 00:45:00 Hrs
Total Marks : 30
    15 x 2 = 30
  1. Identify the quadrant in which an angle of each given measure lies; 250

  2. Identify the quadrant in which an angle of each given measure lies; -550

  3. Two vehicles leave the same place P at the same time moving along two different roads. One vehicle moves at an average speed of 60 km/hr and the other vehicle moves at an average speed of 80 km/hr. After half an hour the vehicle reach the destinations A and B. If AB subtends 60o at the initial point P, then find AB.

  4. Show that \(\frac { (cos\theta -cos3\theta )(sin8\theta +sin2\theta ) }{ (sin5\theta -sin\theta )(cos4\theta -cos6\theta ) } =1\)

  5. For each given Angle, find a coterminal angle with a measure of \(\theta\) such that \(0^o\le \theta \le 360°\) 
    -4500 

  6. Prove that \(sinx+sin2x+sin3x=sin2x(1+2cosx)\)

  7. If sec \(\theta\) + tan \(\theta\) = p, obtain the values of sec \(\theta\), tan \(\theta\) and sin \(\theta\) in terms of p

  8. Prove that sin (45o + \(\theta\)) - sin (45o - \(\theta\)) = \(\sqrt { 2 } \sin { \theta } \)

  9. Find the degree measure corresponding to the following radian measure; \(\frac { \pi }{ 9 } \)

  10. Find the degree measure corresponding to the following radian measure; \(\frac { 2\pi }{ 5 } \)

  11. Evaluate sin\(\left( \frac { -11\pi }{ 3 } \right) \).

  12. If cos A = \(\frac { 4 }{ 5 } \), cos B = \(\frac { 12 }{ 13 } ,\frac { 3\pi }{ 2 } \)\(\pi \), find cos(A + B)

  13. Prove that 2\(cos\left( \frac { \pi }{ 13 } \right) cos\left( \frac { 9\pi }{ 13 } \right) +cos\frac { 3\pi }{ 13 } +cos\frac { 5\pi }{ 13 } \) = 0

  14. Prove that \(\frac { cos9x-cos5x }{ sin17x-sin3x } =-\frac { sin2x }{ cos10x } \)

  15. Find the general solution of \(\sqrt { 3 } \) sec 2x = 2

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