**??? - 2015 JUNE Q9 Answers**

The diagram shows part of the curve

(i) The smallest positive solution of the equation 2cos(1/3

(a) the next smallest positive solution of the equation 2cos(1/3

(b) the smallest positive solution of the equation 2cos(1/3

(ii) The curve

(iii) Calculate the

*y*= 2cos(1/3*x*), where*x*is in radians, and the line*y*=*k*.(i) The smallest positive solution of the equation 2cos(1/3

*x*) =*k*is denoted by*a*. State, in terms of*a*,(a) the next smallest positive solution of the equation 2cos(1/3

*x*) =*k*, [1](b) the smallest positive solution of the equation 2cos(1/3

*x*) = -*k*. [2](ii) The curve

*y*= 2cos(1/3*x*) is shown in the Printed Answer Book. On the diagram, and for the same values of*x*, sketch the curve of*y*= sin(1/3*x*). [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]