??? - 2015 JUNE Q9 Answers
The diagram shows part of the curve y = 2cos(1/3x), where x is in radians, and the line y = k.
(i) The smallest positive solution of the equation 2cos(1/3x) = k is denoted by a. State, in terms of a,
(a) the next smallest positive solution of the equation 2cos(1/3x) = k , [1]
(b) the smallest positive solution of the equation 2cos(1/3x) = -k. [2]
(ii) The curve y = 2cos(1/3x) is shown in the Printed Answer Book. On the diagram, and for the same values of x, sketch the curve of y = sin(1/3x). [2]
(iii) Calculate the x-coordinates of the points of intersection of the curves in part (ii). Give your answers in radians correct to 3 significant figures. [4]
(i) The smallest positive solution of the equation 2cos(1/3x) = k is denoted by a. State, in terms of a,
(a) the next smallest positive solution of the equation 2cos(1/3x) = k , [1]
(b) the smallest positive solution of the equation 2cos(1/3x) = -k. [2]
(ii) The curve y = 2cos(1/3x) is shown in the Printed Answer Book. On the diagram, and for the same values of x, sketch the curve of y = sin(1/3x). [2]
(iii) Calculate the x-coordinates of the points of intersection of the curves in part (ii). Give your answers in radians correct to 3 significant figures. [4]