Math topic中文

Obtuse angles

extending sine and cosine to obtuse angles

Practice questions

  1. 1The points A, B, C, D and E are shown in the diagram below such that ABC and AED are straight lines and BE = 8\sqrt{8}…
  2. 2It is given that y=xsin⁡x+cos⁡2(x2).y = x\sin x + \cos^2\left(\tfrac{x}{2}\right). Obtain an expression for dydx\dfrac{dy}{dx} in the form…
  3. 3Solve the equation 2cosec⁡(x−π3)=−42\cosec\left(x-\dfrac{\pi}{3}\right)=-4 for 0≤x≤2π0\le x\le 2\pi. Solve the equation cot⁡(2x+10∘)=tan⁡70∘\cot(2x+10^\circ)=\tan70^\circ…
  4. 4sin⁡x∘=0.66913\sin x^{\circ} = 0.66913 Given that xx is an obtuse angle, find xx. Answer x = ... cos⁡y∘=−cos⁡121∘\cos y^{\circ} = -\cos 121^{\circ}…
  5. 5Triangle PQR is a right-angled triangle with PQ = 10 cm, QR = 6 cm and ∠PRQ = 90°. M is a point on PR such that MR = 5 P…
  6. 6The diagram shows a semi-circle BAC, with diameter BC = 34 cm. AD and BCD are straight lines. Given that cos⁡∠ABC=817\cos\angle ABC = \dfrac{8}{17}…
  7. 7Given that 0<x<1800 < x < 180, find the possible values of xx for sin⁡x∘=0.985\sin x^{\circ} = 0.985. Give your answers correct to 1 d…
  8. 8The diagram shows a rectangular table ABCD arranged such that the side AD is inclined at an angle of θ\theta to the wal…
  9. 9The sine of an obtuse angle is 5/135/13. Without the use of a calculator, find the value for the cosine of the same angle.…
  10. 10Given that cos⁡(A+B)=−513\cos(A+B)= -\dfrac{5}{13} and sin⁡Asin⁡B=1526\sin A\sin B=\dfrac{15}{26}, where A and B are acute angles and angle A > a…
  11. 11The figure shows ΔABC. May said that the line AC intersect the y axis at 3.2. Show how you would check if she is correct…
  12. 12ABC is a right-angled triangle with ∠ABC=90∘\angle ABC = 90^\circ, AB=8AB = 8 cm and BC=15BC = 15 cm. Find the value of cos⁡∠BCD\cos \angle BCD…
  13. 13In the diagram, XYZ is a straight line. AY = 20 m, AZ = 12 m and YZ = 16 m. The ratio of XY : YZ is 1 : 4. Prove that tr…
  14. 14The sine of an angle is 0.60.6, find the two possible values for angle.
  15. 15In the diagram, A is an obtuse angle such that sin⁡A=513\sin A = \tfrac{5}{13}. Leaving your answer as a fraction, find the val…