Math topic中文

Radian measure

use of radian measure of angle (including conversion between radians and degrees)

Practice questions

  1. 1In the diagram, POR is a quadrant of a circle with radius 6 cm. OR and PQ are parallel. QR is an arc of a circle with ce…
  2. 2A circle with centre O has a tangent XY at D. ∠ODC = 70°, ∠BCD = 120° and ∠ODA = 15°. Find ∠CDY. Find ∠DAB. Find ∠OBA. T…
  3. 3In the diagram, AB is a tangent to the circle with centre O, ∠CAB = 58° and CDE is a straight line. Find, stating your r…
  4. 4The diagram shows a cardboard in the shape of a major sector, centre O and radius 15 cm. The total area of the major sec…
  5. 5In the diagram, OAB is a sector of a circle with centre O. Given that OA = 12 cm, ∠AOB = θ\theta radians, OC = 8 cm and…
  6. 6The diagram shows four identical blades of a fan, whose centre is O. Arc AB on the fan blade forms an angle of π/6\pi/6 a…
  7. 7Convert 40° into radians. Leave your answers in terms of π\pi. Answer ... radians Convert 23 km/h into m/s. Answer ...…
  8. 8The diagram shows the cross section of a plastic pipe. The arc AB is part of the circle with centre O and radius 45 mm.…
  9. 9A, B and C are points on the circle centre O and AB = BC. P is the midpoint of chord AB and Q is the midpoint of chord B…
  10. 10In the diagram, OAPB is a sector of circle with centre O and radius 9 cm. Angle AOB = 1.4 radians. C is the centre of th…
  11. 11The diagram shows a triangle ABC with AB produced to D. AB=18 cmAB = 18\,\mathrm{cm}, BC=20 cmBC = 20\,\mathrm{cm}, AC=22 cmAC = 22\,\mathrm{cm}…
  12. 12The diagram shows a circle, centre O, radius 10 cm. AB is a chord of length 16 cm. Show that angle AOB = 1.855 radians,…
  13. 13设扇形的圆心角为αα，半径为rr，弧长为ll，面积为SS，周长为LL，则()(\quad) A. 若αα，rr确定，则LL，SS唯一确定 B. 若αα，ll确定，则LL…
  14. 14A semicircle OABCDE with centre O has a radius of 4.5 cm. Chord BD has a length of 6 cm and the perimeter of minor secto…
  15. 15The diagram shows a circle of radius 8 cm and centre O. The tangent to the circle at T meets OA produced at R and OB pro…
  16. 16X, Y and Z lie on a circle with centre O and radius 44 cm. Angle XOY = 2.52.5 radians. [Figure as described below] Find…
  17. 17欧拉公式eix=cos⁡x+isin⁡x(ie^{ix}=\cos x+i\sin x(i为虚数单位))是由瑞士著名数学家欧拉发明的，它被誉为“数学中的天桥”．根据欧拉公式可知，e2ie^{2i}表示的复数在复平面中位于()(\quad) A. 第一象限…