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11th Standard English Medium Maths Subject Trigonometry Book Back 3 Mark Questions with Solution Part - II

11th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 30

    3 Marks

    10 x 3 = 30
  1. In a circular of diameter 40 cm, a chord is of length 20 cm. FInd the length of the minor arc of the chord?

  2. A train is moving on a circular track of 1500 m radius at the rate of 66 Km/hr. What angle will it turn in 20 seconds?

  3. Prove that cos (A + B) cos C - cos (B + c) cos A = sin B sin (C - A)

  4. Find the degree measure of the angle subtended at the center of circle of radius 100 cm by an arc of length 22 cm.

  5. Prove that sin2 (A + B) - sin2 (A - B) = sin 2A sin 2B

  6. The perimeter of a certain sector of a circle is equal to the length of the arc of a semi-circle having the same radius. Express the angle of the sector in degree, minites and seconds,

  7. If tan x = \(\frac{n}{n+1}\) and tan y = \(\frac{1}{2n+1}\), find tan (x + y).

  8. If \(\theta +\phi =\alpha\)  and \(tan​​\theta=k\ \tan\ \phi \) then prove that \(\sin { \left( \theta -\phi \right) } =\frac { k-1 }{ k+1 } \sin { \alpha } \).

  9. \(\left( \frac { 5 }{ 7 } ,\frac { 2\sqrt { 6 } }{ 7 } \right) \) is a point on the terminal side of an angle \(\theta\) in standard position. Determine the six trigonometric function values of angle \(\theta\)

  10. If \(\theta\) is an acute angle, then find \(\sin { \left( \frac { \pi }{ 4 } -\frac { \theta }{ 2 } \right) } \), when \(\sin { \theta } =\frac { 1 }{ 25 } \)

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