Transcription of Core Mathematics C2 Advanced Subsidiary Trigonometry
1 Edexcel GCECore Mathematics C2 Advanced SubsidiaryTrigonometryMaterials required for examination Items included with question papersMathematical Formulae (Pink or Green) NilAdvice to CandidatesYou must ensure that your answers to parts of questions are clearly must show sufficient working to make your methods clear to the Examiner. Answers without working may not gain full (a)Show that the equation 5 cos2 x = 3(1 + sin x)can be written as5 sin2 x + 3 sin x 2 = 0.(2)(b)Hence solve, for 0 x < 360 , the equation5 cos2 x = 3(1 + sin x),giving your answers to 1 decimal place where appropriate.(5)22.(a)Show that the equation3 sin2 2 cos2 = 1can be written as5 sin2 = 3.(2)(b)Hence solve, for 0 < 360 , the equation3 sin2 2 cos2 = 1,giving your answer to 1 decimal place.(7) all the solutions, in the interval 0 x < 2 , of the equation2 cos2 x + 1 = 5 sin x,giving each solution in terms of.
2 (6)4.(a)Given that sin = 5 cos , find the value of tan .(1)(b)Hence, or otherwise, find the values of in the interval 0 < 360 for whichsin = 5 cos ,giving your answers to 1 decimal place. (3) , for 0 x 180 , the equation(a)sin (x + 10 ) = 23 ,(4)(b)cos 2x = , giving your answers to 1 decimal place.(4)56.(a)Show that the equation4 sin2 x + 9 cos x 6 = 0can be written as4 cos2 x 9 cos x + 2 = 0.(2)(b) Hence solve, for 0 x < 720 ,4 sin2 x + 9 cos x 6 = 0,giving your answers to 1 decimal place. (6)67.(i) Solve, for 180 < 180 ,(1 + tan )(5 sin 2) = 0.(4)(ii) Solve, for 0 x < 360 ,4 sin x = 3 tan x.(6)78.(a)Find all the values of , to 1 decimal place, in the interval 0 < 360 for which5 sin ( + 30 ) = 3. (4)(b)Find all the values of , to 1 decimal place, in the interval 0 < 360 for whichtan2 = 4.(5) , for 0 x < 360 ,(a)sin(x 20 ) = 21 ,(4)(b) cos 3x = 21.
3 (6)910.(a)Sketch, for 0 x 2 , the graph of y = sin +6 x.(2) (b)Write down the exact coordinates of the points where the graph meets the coordinate axes. (3)(c)Solve, for 0 x 2 , the equationsin +6 x = ,giving your answers in radians to 2 decimal places.(5) 10
