ࡱ> =Y &bjbjWW b==4EY]444HHHH8DlH<Tl7777679;$=?r<4<qTqqq 47HH7qq Z1L ~470$sHHI(7z 1. a) Solve the equation sin2x = sinx for 0(x<360: [6] b) Hence write down the solutions to sin4x = sin2x for 0(x<180 [3] 2. Given that sinA =  EMBED Equation.2  and sinB =  EMBED Equation.2 , where A and B are acute angles, find, without using a calculator and giving your answers as fractions, the value of: a) sin(A+B) [5] b) cos2A [3] 3. Eliminate q from the pair of equations a) a = 2cosq b=cos2q [3] b) a=cos2q b= sinq + 2 [3] c) a = 2+sin2q b=sinq [4] 4. a) Prove that cos3A ( 4cos3A - 3cosA [7] b) Hence obtain the solutions to the equation cos3A + 2cosA = 0 0(A(p [5] 5. a) Obtain the solution to: 2cosx cos60 = 2sinx sin60 + 1 0o (x(360o [6] b) Hence or otherwise, obtain the solution to: i) 2cos EMBED Equation.3 xcos60 = 2sin EMBED Equation.3 xsin60 + 1 0o (x(360o [2] ii) 2cos(x-30)cos60 = 2sin(x-30)sin60 + 1 0o (x(360o [2] 6. Without using a calculator, find the value of: a) sin50ocos10o + sin10ocos50o [2] b) cos75ocos15o-sin75osin15o [2] c) EMBED Equation.3  [2] d) 2sin75ocos75o [2] e) cos215o  sin215o [2] Give your answers in surd form where appropriate 7. Solve a) 6sin EMBED Equation.3 x cos EMBED Equation.3 x + cosx = 0 0o0 and 0<a<90o [4] b) Hence solve for 0(x<360o the equation cosx + 7sinx = 5. [4] 21. a) Express 2sinx + 3cosx in the form Rsin(x+a) where R is positive and 0<a<90o [4] b) Hence find the maximum and minimum values of 2sinx + 3cosx + 4, giving your answer in surd form [3] 22. a) Given that cos(x+40o) = 3sin(x+500), show that tanx = -0.5959 correct to 4 decimal places [4] b) Hence find the values of x in the interval 0 (x<360o for which cos(x+40o) = 3sin(x+50o), giving your answers correct to 1 decimal place [3] 23. a) Express cos2x - (3sin2x in the form Rcos(2x+a), where R >0 and 0 < a <90o [4] b) Hence sketch the curve y = cos2x - (3sin2x for 0(x(3600, showing intersections with the coordinate axes and maximum and minimum points. 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