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Trigonometric Ratios and Their Application

1. If we convert 135° to radian measure, we get
   A.3π/4 B.3π/2 C.π/4 D.π/2 E.(3+π)/2
2. 75° in radian measure is
   A.π/75 B.75/π C.5π/12 D.12π/5 E.π/30
   3.An arc PQ subtends an angle 60° at the centre O of radius 3 cm. The area of the sector POQ is
   A. 270 〖cm〗^2 B. 3/2 〖cm〗^2 C. 3π/2 〖cm〗^2 D. 3π 〖cm〗^2 E. 180 〖cm〗^2
   4.A sector of a circle has arc length of 8 cm and the area of 16 cm2,then the radius of the circle
   in cm , is
   A. 2 B. 3 C.5 D. 48 E. 12
3. OAB is a sector of a circle with centre O, radius 8 cm and a perimeter 22 cm. Then the area
   of sector, in square cm is
   A. 6 B. 28 C. 24 D. 48 E. 12
4. The area , in cm2 , of a circle has the same numerical value as the circumference, in cm, of
   the same circle. The radius , in cm, is
   A. 2 B. 1 C.2/π D.1/π E.1/2
5. An arc PQ subtends an angle of 120° at the centre of a circle of radius 1 cm. The length of
   arc PQ is
   A. 120 cm B. 60 cm C. π/6cm D. 2π/3cm E.π^2/18 cm
6. If the central angle of a circle of radius 14 cm cuts off an arc of length 28 cm , then the radian
   measure of the angle is
   A. 2√2 B.2 C.1 D. 4 E. 8π
7. The pendulum on a clock swings through an angle of 2 radians, and the tip sweeps out and
   arc of 6 inches. Then the length of the pendulum is
   A. 3 inches B. 12 inches C. 24 inches D. 12/π inches E. 24/π inches
8. The area of a sector of a circle is 143 cm2and the length of the arc of the sector is 11 cm .
   Then the radius , in cm, of the circle is
   A. 11 B.13/2 C.26 D. 13 E. None of these
9. The figure shows a sector OMN of a circle at centre O with the radius r = 6 cm and a
   perimeter of 16 cm . The area of sector MON = ………
   A. 24〖cm〗^2 B. 36〖cm〗^2 C. 15〖cm〗^2 D.12〖cm〗^2 E. 9〖cm〗^2

12.An arc BC subtends an angle of 144° at the centre O if a circle of radius 10 cm . Then the
length of arc BC is
A.25/2π B.25/2 π C.8/π D.π/8 E. 8π
acute, then cos θ=……….
A.√3/2 B.1/2 C.√2/3 D.√8/3 E.2/√3