*H31123A0228* 1. (a) Find the value of at the point where x = 2 on the curve with equation. y = x 2 (5x 1). (6)

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1 C3 past papers 009 to 01 physicsandmathstutor.comthis paper: January 009 If you don't find enough space in this booklet for your working for a question, then pleasecuse some loose-leaf paper and glue it into the booklet at the appropriate point. dy 1. (a) Find the value of at the point where x = on the curve with equation dx y = x (5x 1). sin x (b) Differentiate with respect to x. x (6) (4) *H3113A08*

2 physicsandmathstutor.com January 009. f( x) = x + x x x x 3 (a) Express f (x) as a single fraction in its simplest form. (4) (b) Hence show that f() x = ( x ) 3 4 *H3113A048*

3 physicsandmathstutor.com January y 5 T (3, 5) S (7, ) O 3 7 x Figure 1 Figure 1 shows the graph of y = f (x), 1 < x < 9. The points T(3, 5) and S(7, ) are turning points on the graph. Sketch, on separate diagrams, the graphs of (a) y = f (x) 4, (b) y = f( x). Indicate on each diagram the coordinates of any turning points on your sketch. 8 *H3113A088*

4 physicsandmathstutor.com January Find the equation of the tangent to the curve π x= cos( y+ π ) at 0,. 4 Give your answer in the form y = ax + b, where a and b are constants to be found. (6) 10 *H3113A0108*

5 physicsandmathstutor.com January The functions f and g are defined by (a) Write down the range of g. (b) Show that the composite function fg is defined by fg : x x + 3e x, x R. (c) Write down the range of fg. d (d) Solve the equation fg x x xe x ( ) ( + ). dx = (1) () (1) (6) 1 *H3113A018*

6 physicsandmathstutor.com January (a) (i) By writing 3θ = (θ + θ), show that (ii) Hence, or otherwise, for Give your answers in terms of π. sin 3θ = 3 sin θ 4 sin 3 θ. π 0 < θ < 3, solve 8 sin 3 θ 6 sin θ + 1 = 0. (4) (5) (b) Using sin( θ α) = sin θcosα cosθsin α, or otherwise, show that 1 sin15 = ( 6 ). 4 (4) 16 *H3113A0168*

7 7. The curve with equation y = f (x) has a turning point P. physicsandmathstutor.com January 009 f( x) = 3xe x 1 (a) Find the exact coordinates of P. (5) The equation f (x) = 0 has a root between x = 0.5 and x = 0.3 (b) Use the iterative formula x n = 3 e with x 0 = 0.5 to find, to 4 decimal places, the values of x 1, x and x 3. x n (c) By choosing a suitable interval, show that a root of f (x) = 0 is x = correct to 4 decimal places. 0 *H3113A008*

8 physicsandmathstutor.com January (a) Express 3 cos θ + 4 sin θ in the form R cos(θ α), where R and α are constants, R > 0 and 0 < α < 90. (4) (b) Hence find the maximum value of 3 cos θ + 4 sin θ and the smallest positive value of θ for which this maximum occurs. The temperature, f (t), of a warehouse is modelled using the equation f (t) = cos(15t) + 4 sin(15t), where t is the time in hours from midday and 0 t < 4. (c) Calculate the minimum temperature of the warehouse as given by this model. (d) Find the value of t when this minimum temperature occurs. () 4 *H3113A048*

9 1. physicsandmathstutor.com C3 June 009 y A 1 O x Figure 1 Figure 1 shows part of the curve with equation x-axis at the point A where x = α. y x x 3 = + +, which intersects the To find an approximation to α, the iterative formula is used. x + = + n 1 ( xn ) (a) Taking x 0 =.5, find the values of x 1, x, x 3 and x 4. Give your answers to 3 decimal places where appropriate. (b) Show that α =.359 correct to 3 decimal places. *H3464A08*

10 physicsandmathstutor.com June 009. (a) Use the identity cos θ + sin θ = 1 to prove that tan θ = sec θ 1. (b) Solve, for 0 θ < 360, the equation tan θ + 4 sec θ + sec θ = () (6) 4 *H3464A048*

11 physicsandmathstutor.com June Rabbits were introduced onto an island. The number of rabbits, P, t years after they were introduced is modelled by the equation 5 P = 80e 1 t, t, t 0 (a) Write down the number of rabbits that were introduced to the island. (1) (b) Find the number of years it would take for the number of rabbits to first exceed () (c) Find d P. dt (d) Find P when d P = 50. dt () 6 *H3464A068*

12 physicsandmathstutor.com June (i) Differentiate with respect to x (a) (b) x cos3x ln( x + 1) x + 1 (4) (ii) A curve C has the equation y= ( 4x+ 1 ), x >, y > 0 The point P on the curve has x-coordinate. Find an equation of the tangent to C at P in the form ax + by + c = 0, where a, b and c are integers. (6) *H3464A0108*

13 5. physicsandmathstutor.com June 009 y O B x A Figure Figure shows a sketch of part of the curve with equation y = f(x), x. 1 The curve meets the coordinate axes at the points A(0,1 k) and B ( ln k,0 ), where k is a constant and k > 1, as shown in Figure. On separate diagrams, sketch the curve with equation (a) y = f( x), (b) y = 1 f ( x). () Show on each sketch the coordinates, in terms of k, of each point at which the curve meets or cuts the axes. Given that x f( x) = e k, (c) state the range of f, (1) (d) find 1 f ( x), (e) write down the domain of 1 f. (1) 14 *H3464A0148*

14 physicsandmathstutor.com June (a) Use the identity cos( A+ B) = cos Acos B sin Asin B, to show that cos A = 1 sin A () The curves C 1 and C have equations C 1 : y = 3sinx C : y = 4sin x cos x (b) Show that the x-coordinates of the points where C 1 and C intersect satisfy the equation 4cos x + 3sin x = (c) Express 4cosx + 3sinx in the form R cos (x α), where R > 0 and 0 < α < 90, giving the value of α to decimal places. (d) Hence find, for 0 x < 180, all the solutions of 4cos x + 3sin x = giving your answers to 1 decimal place. (4) 18 *H3464A0188*

15 physicsandmathstutor.com June The function f is defined by x 8 f( x) = 1 +, ( x + 4) ( x )( x + 4) x x 4, x x 3 (a) Show that f( x) = x (5) The function g is defined by x e 3 g( x) =, x e x, x ln x e (b) Differentiate g( x) to show that g( x) = x (e ) (c) Find the exact values of x for which g( x) = 1 (4) *H3464A08*

16 physicsandmathstutor.com June (a) Write down sin x in terms of sin x and cos x. (b) Find, for 0 < x < π, all the solutions of the equation cosec x 8cos x = 0 (1) giving your answers to decimal places. (5) 6 *H3464A068*

17 physicsandmathstutor.com C3 January Express x + 1 3x 3 1 3x+ 1 as a single fraction in its simplest form. (4) *N35381A08*

18 . 3 f( x) = x + x 3x 11 (a) Show that f(x) = 0 can be rearranged as physicsandmathstutor.com January 010 x = 3x + 11, x. x + () The equation f(x) = 0 has one positive root α. x The iterative formula x = 3 n + 11 n+ 1 xn + is used to find an approximation to α. (b) Taking x 1 = 0, find, to 3 decimal places, the values of x, x 3 and x 4. (c) Show that α =.057 correct to 3 decimal places. 4 *N35381A048*

19 physicsandmathstutor.com January (a) Express 5 cos x 3 sin x in the form R cos(x + α), where R > 0 and 0 < α < 1 π. (4) (b) Hence, or otherwise, solve the equation 5 cos x 3 sin x = 4 for 0 x <, giving your answers to decimal places. (5) 6 *N35381A068*

20 physicsandmathstutor.com January 010 ln ( x + 1 ) dy 4. (i) Given that y =, find x dx. (4) (ii) Given that x = tan y, show that d y 1 = dx + 1 x. (5) 8 *N35381A088*

21 physicsandmathstutor.com January Sketch the graph of y = ln x, stating the coordinates of any points of intersection with the axes. 1 *N35381A018*

22 physicsandmathstutor.com January y A(, 3) 1 O x Figure 1 Figure 1 shows a sketch of the graph of y = f (x). The graph intersects the y-axis at the point (0, 1) and the point A(, 3) is the maximum turning point. Sketch, on separate axes, the graphs of (i) y = f( x) + 1, (ii) y = f(x + ) + 3, (iii) y = f(x). On each sketch, show the coordinates of the point at which your graph intersects the y-axis and the coordinates of the point to which A is transformed. (9) 14 *N35381A0148*

23 physicsandmathstutor.com January (a) By writing sec x as Given that y = e x sec 3x, (b) find d y dx. 1 d(sec x), show that = sec xtan x. cos x dx (4) The curve with equation y = e x sec 3x, < x < 6 (a, b). π π 6, has a minimum turning point at (c) Find the values of the constants a and b, giving your answers to 3 significant figures. (4) 18 *N35381A0188*

24 8. Solve physicsandmathstutor.com January 010 cosec x cot x = 1 for 0 x 180. (7) *N35381A08*

25 physicsandmathstutor.com January (i) Find the exact solutions to the equations (a) ln (3x 7) = 5 (b) 3 x e 7x + = 15 (5) (ii) The functions f and g are defined by f (x) = e x + 3, x g(x) = ln (x 1), x, x > 1 (a) Find f 1 and state its domain. (4) (b) Find fg and state its range. 4 *N35381A048*

26 physicsandmathstutor.com C3 June (a) Show that sin θ = tanθ 1+ cos θ () (b) Hence find, for 180 θ < 180, all the solutions of sin θ = 1 1+ cos θ Give your answers to 1 decimal place. *H35385A08*

27 physicsandmathstutor.com June 010. A curve C has equation 3 y = (5 3x), 5 x 3 The point P on C has x-coordinate. Find an equation of the normal to C at P in the form ax + by + c = 0, where a, b and c are integers. (7) 4 *H35385A048*

28 physicsandmathstutor.com June f( x) = 4cosec x 4x+ 1, where x is in radians. (a) Show that there is a root α of f( x ) = 0 in the interval [1., 1.3]. () (b) Show that the equation f( x ) = 0 can be written in the form 1 1 x = + sin x 4 () (c) Use the iterative formula 1 1 x n+ 1 = +, x 0 = 1.5, sin x 4 n to calculate the values of x 1, x and x 3, giving your answers to 4 decimal places. (d) By considering the change of sign of f( x) in a suitable interval, verify that α = 1.91 correct to 3 decimal places. () 6 *H35385A068*

29 physicsandmathstutor.com June The function f is defined by f: xa x 5, (a) Sketch the graph with equation y = f( x), showing the coordinates of the points where the graph cuts or meets the axes. () (b) Solve f( x) = 15 + x. The function g is defined by g: x x 4x+ 1 a,, 0 x 5 (c) Find fg(). (d) Find the range of g. () 10 *H35385A0108*

30 physicsandmathstutor.com June y C O x Figure 1 Figure 1 shows a sketch of the curve C with the equation y = x x+ x ( 5 )e. (a) Find the coordinates of the point where C crosses the y-axis. (1) (b) Show that C crosses the x-axis at x = and find the x-coordinate of the other point where C crosses the x-axis. (c) Find d y. dx (d) Hence find the exact coordinates of the turning points of C. (5) 14 *H35385A0148*

31 physicsandmathstutor.com June y 5 O x A(3, 4) Figure Figure shows a sketch of the curve with the equation y = f( x),. The curve has a turning point at A (3, 4) and also passes through the point (0, 5). (a) Write down the coordinates of the point to which A is transformed on the curve with equation (i) y = f( x), (ii) y = f ( 1 x). (4) (b) Sketch the curve with equation On your sketch show the coordinates of all turning points and the coordinates of the point at which the curve cuts the y-axis. The curve with equation y = f( x) is a translation of the curve with equation y = x. (c) Find f( x). (d) Explain why the function f does not have an inverse. () (1) 18 *H35385A0188*

32 physicsandmathstutor.com June 010 π 7. (a) Express sin θ 1.5 cos θ in the form R sin (θ α), where R > 0 and 0 < α <. Give the value of α to 4 decimal places. (b) (i) Find the maximum value of sin θ 1.5 cos θ. (ii) Find the value of θ, for 0 θ < π, at which this maximum occurs. Tom models the height of sea water, H metres, on a particular day by the equation 4πt 4πt H = 6+ sin 1. 5cos 5 5, 0 t < 1, where t hours is the number of hours after midday. (c) Calculate the maximum value of H predicted by this model and the value of t, to decimal places, when this maximum occurs. (d) Calculate, to the nearest minute, the times when the height of sea water is predicted, by this model, to be 7 metres. (6) *H35385A08*

33 physicsandmathstutor.com June (a) Simplify fully x + 9x 5 x + x 15 Given that ln( x + 9x 5) = 1+ ln( x + x 15), x 5, (b) find x in terms of e. (4) 6 *H35385A068*

34 physicsandmathstutor.com C3 January (a) Express 7cos x 4sin x in the form R cos (x + ) where R 0 and 0 π. Give the value of to 3 decimal places. (b) Hence write down the minimum value of 7 cos x 4 sin x. (c) Solve, for 0 x, the equation 7cos x 4sin x= 10 (1) giving your answers to decimal places. (5) *H35404RA08*

35 . (a) Express physicsandmathstutor.com January 011 4x 1 3 ( x 1) ( x 1)(x 1) as a single fraction in its simplest form. (4) Given that f( x) 4x 1 3 = ( x 1) ( x 1)(x 1), x 1, (b) show that f( x) = 3 x 1 () (c) Hence differentiate f (x) and find f (). 4 *H35404RA048*

36 physicsandmathstutor.com January Find all the solutions of cos = 1 sin in the interval (6) 8 *H35404RA088*

37 physicsandmathstutor.com January Joan brings a cup of hot tea into a room and places the cup on a table. At time t minutes after Joan places the cup on the table, the temperature, C, of the tea is modelled by the equation = 0 + Ae kt, where A and k are positive constants. Given that the initial temperature of the tea was 90 C, (a) find the value of A. () The tea takes 5 minutes to decrease in temperature from 90 C to 55 C. (b) Show that 1 k = ln. 5 (c) Find the rate at which the temperature of the tea is decreasing at the instant when t = 10. Give your answer, in C per minute, to 3 decimal places. 10 *H35404RA0108*

38 physicsandmathstutor.com January y Q O A B x Figure 1 Figure 1 shows a sketch of part of the curve with equation y = f( x), where f( x) = (8 x)ln x, x 0 The curve cuts the x-axis at the points A and B and has a maximum turning point at Q, as shown in Figure 1. (a) Write down the coordinates of A and the coordinates of B. (b) Find f( x). (c) Show that the x-coordinate of Q lies between 3.5 and 3.6 (d) Show that the x-coordinate of Q is the solution of 8 x = 1 + lnx () () To find an approximation for the x-coordinate of Q, the iteration formula is used. 8 xn+ 1 = 1 + lnx n (e) Taking x 0 = 3.55, find the values of x 1, x and x. 3 Give your answers to 3 decimal places. 14 *H35404RA0148*

39 physicsandmathstutor.com January The function f is defined by f: x 3 x x 5, x, x 5 (a) Find 1 f ( x). y 4 1 O 8 x 6 9 Figure The function g has domain 1 x 8, and is linear from ( 1, 9) to (, 0) and from (, 0) to (8, 4). Figure shows a sketch of the graph of y = g(x). (b) Write down the range of g. (c) Find gg(). (d) Find fg(8). (e) On separate diagrams, sketch the graph with equation (1) () () (i) y = g( x), (ii) y = 1 g ( x). Show on each sketch the coordinates of each point at which the graph meets or cuts the axes. (4) 1 (f) State the domain of the inverse function g. (1) 18 *H35404RA0188*

40 physicsandmathstutor.com January The curve C has equation y 3+ sinx = + cos x (a) Show that dy 6sinx+ 4cosx+ = dx cos ( + x) (4) (b) Find an equation of the tangent to C at the point on C where x = π. Write your answer in the form y = ax + b, where a and b are exact constants. (4) *H35404RA08*

41 8. (a) Given that physicsandmathstutor.com January 011 d ( cos x) = sin x dx show that ( ) d sec x = sec x tan x. dx Given that x = sec y (b) find d x dy in terms of y. () (c) Hence find d y dx in terms of x. (4) 6 *H35404RA068*

42 physicsandmathstutor.com C3 June Differentiate with respect to x (a) ln ( x + 3x+ 5) (b) cos x x () *P38159A04*

43 physicsandmathstutor.com June 011. f( x ) = sinn( x ) + x, 0 x (a) Show that f (x) = 0 has a root between x = 0.75 and x = 0.85 ( ) The equation f (x) = 0 can be written as x = arcsin x 1. () (b) Use the iterative formula x n + = ( xn) 1 arcsin 1 05., x 0 = to find the values of x 1, x and x 3, giving your answers to 5 decimal places. (c) Show that = is correct to 5 decimal places. 4 *P38159A044*

44 physicsandmathstutor.com June y O 3 4 R Figure 1 x Figure 1 shows part of the graph of y = f (x), x. The graph consists of two line segments that meet at the point R (4, 3 ), as shown in Figure 1. Sketch, on separate diagrams, the graphs of (a) y = f (x + 4), (b) y = f( x). On each diagram, show the coordinates of the point corresponding to R. 6 *P38159A064*

45 physicsandmathstutor.com June The function f is defined by f : x 4 ln ( x + ), x, x 1 (a) Find f 1 ( x). (b) Find the domain of f 1. (1) The function g is defined by x g: x e, x (c) Find fg (x), giving your answer in its simplest form. (d) Find the range of fg. (1) 8 *P38159A084*

46 physicsandmathstutor.com June The mass, m grams, of a leaf t days after it has been picked from a tree is given by m= pe kt where k and p are positive constants. When the leaf is picked from the tree, its mass is 7.5 grams and 4 days later its mass is.5 grams. (a) Write down the value of p. (1) (b) Show that k = 1 ln 3. 4 (4) (c) Find the value of t when d m = 06. ln3. dt (6) 10 *P38159A0104*

47 physicsandmathstutor.com June (a) Prove that 1 cos θ = tan θ, θ 90n, n Z sin θ sin θ (4) (b) Hence, or otherwise, (i) show that tan 15 = 3, (ii) solve, for 0 x 360, cosec 4x cot 4x = 1 (5) 1 *P38159A014*

48 physicsandmathstutor.com June f ( x) = 4x 5 x, x ± 3, x 1 ( x+ 1)( x 3) x 9 (a) Show that f( x) = 5 ( x+ 1)( x+ 3) (5) 5 The curve C has equation y = f (x). The point P 1, lies on C. (b) Find an equation of the normal to C at P. (8) 16 *P38159A0164*

49 physicsandmathstutor.com June (a) Express cos 3x 3sin 3x in the form R cos (3x + ), where R and are constants, R 0 and 0 < α < π. Give your answers to 3 significant figures. (4) x f( x) = e cos3x (b) Show that f (x) can be written in the form f() x = Re x cos( 3x + α ) where R and are the constants found in part (a). (5) (c) Hence, or otherwise, find the smallest positive value of x for which the curve with equation y = f (x) has a turning point. 0 *P38159A004*

50 physicsandmathstutor.com C3 January Differentiate with respect to x, giving your answer in its simplest form, (a) x ln ( 3x) (4) (b) sin 4x 3 x (5) *P40084A04*

51 . physicsandmathstutor.com January 01 y P( 3, 0) O x Q(, 4) Figure 1 Figure 1 shows the graph of equation y = f (x). The points P ( 3, 0) and Q (, 4) are stationary points on the graph. Sketch, on separate diagrams, the graphs of ( ) (a) y = 3f x+ (b) y = f ( x) On each diagram, show the coordinates of any stationary points. 4 *P40084A044*

52 physicsandmathstutor.com January The area, A mm, of a bacterial culture growing in milk, t hours after midday, is given by A = 0e 15t., t 0 (a) Write down the area of the culture at midday. (1) (b) Find the time at which the area of the culture is twice its area at midday. Give your answer to the nearest minute. (5) 6 *P40084A064*

53 physicsandmathstutor.com January 01 π π 4. The point P is the point on the curve x= tan y+ with y-coordinate. 1 4 Find an equation of the normal to the curve at P. (7) 8 *P40084A084*

54 physicsandmathstutor.com January Solve, for 0 180, cot 3 7 cosec 3 5 Give your answers in degrees to 1 decimal place. (10) 10 *P40084A0104*

55 physicsandmathstutor.com January 01 ( )= + ( ) 6. f x x 3x cos 1 x, 0 x (a) Show that the equation f (x) = 0 has a solution in the interval 0.8 < x < 0.9 () The curve with equation y = f (x) has a minimum point P. (b) Show that the x-coordinate of P is the solution of the equation x x = 3 + ( 1 sin ) (4) (c) Using the iteration formula x n xn + = + ( 1 3 sin ) 1, x0 = find the values of x 1, x and x 3, giving your answers to 3 decimal places. (d) By choosing a suitable interval, show that the x-coordinate of P is correct to 4 decimal places. 1 *P40084A014*

56 physicsandmathstutor.com January The function f is defined by ( ) x f: x , x, x x + 7x 4 R > x+ 4 1 (a) Show that f ( x )= x 1 (4) (b) Find f 1 ( x ) (c) Find the domain of f 1 (1) g( x)= ln x+ 1 ( ) (d) Find the solution of fg ( x )= 1 7, giving your answer in terms of e. (4) 16 *P40084A0164*

57 physicsandmathstutor.com January (a) Starting from the formulae for sin ( A + B ) and cos ( A + B ), prove that (b) Deduce that tan A+ tan B tan ( A+ B)= 1 tan Atan B π 1+ 3tanθ tan θ + = 6 3 tanθ (4) (c) Hence, or otherwise, solve, for 0 θ π, tan ( tan ) tan ( ) 1+ 3 θ = 3 θ π θ Give your answers as multiples of (6) 0 *P40084A004*

58 physicsandmathstutor.com C3 June Express 3 ( x + ) 9x 4 3x+ 1 as a single fraction in its simplest form. (4) *P40686RA03*

59 physicsandmathstutor.com June f( x) = x + 3x + 4x 1 (a) Show that the equation f( x ) = 0 can be written as x x = + x 43 ( ), x 3 ( 3 ) 3 The equation x + 3x + 4x 1 = 0 has a single root which is between 1 and (b) Use the iteration formula x x = n n+ 43 ( ) 1 ( 3 + xn ), n 0 with x 0 = 1 to find, to decimal places, the value of x, x and x 3. 1 The root of f( x ) = 0 is. (c) By choosing a suitable interval, prove that α = 1. 7 to 3 decimal places. 4 *P40686RA043*

60 3. physicsandmathstutor.com June 01 y P C O x Figure 1 Figure 1 shows a sketch of the curve C which has equation x y = e 3 sin 3x, π x π 3 3 (a) Find the x coordinate of the turning point P on C, for which x 0 Give your answer as a multiple of. (6) (b) Find an equation of the normal to C at the point where x = 0 8 *P40686RA083*

61 4. physicsandmathstutor.com June 01 y Q (0, 5) P ( 1.5, 0) O x Figure Figure shows part of the curve with equation y = f( x) The curve passes through the points P( 1. 5, 0) and Q( 0, 5 ) as shown. On separate diagrams, sketch the curve with equation (a) y (b) y (c) y = f( x) = f( x) = f( 3x) () () Indicate clearly on each sketch the coordinates of the points at which the curve crosses or meets the axes. 1 *P40686RA013*

62 physicsandmathstutor.com June (a) Express 4cosec θ cosec θ in terms of sin and cos. () (b) Hence show that 4cosec θ cosec θ = sec θ (c) Hence or otherwise solve, for 0 < <, giving your answers in terms of. 4cosec θ cosec θ = 4 (4) 16 *P40686RA0163*

63 physicsandmathstutor.com June The functions f and g are defined by x f : x e +, x g: x lnx, x 0 (a) State the range of f. (b) Find fg( x ), giving your answer in its simplest form. (c) Find the exact value of x for which f( x + 3) = 6 (d) Find f 1, the inverse function of f, stating its domain. (1) () (4) (e) On the same axes sketch the curves with equation y = f( x) and y = f 1 ( x), giving the coordinates of all the points where the curves cross the axes. (4) 0 *P40686RA003*

64 physicsandmathstutor.com June (a) Differentiate with respect to x, 1 (i) x ln( 3x) (ii) 1 10x ( x 1), giving your answer in its simplest form. 5 (6) (b) Given that x = 3tan y find d y dx in terms of x. (5) 4 *P40686RA043*

65 physicsandmathstutor.com June f ( x) = 7 cos x 4sin x Given that f( x) = Rcos( x+ α ), where R 0 and 0< α < 90, (a) find the value of R and the value of. (b) Hence solve the equation 7cos x 4sin x= 1. 5 for 0 x 180, giving your answers to 1 decimal place. (c) Express 14cos x 48sin xcos x in the form acos x+ bsin x+ c, where a, b, and c are constants to be found. (5) () (d) Hence, using your answers to parts (a) and (c), deduce the maximum value of 14cos x 48sin xcos x () 8 *P40686RA083*