Trigonometric functions — Paper 2 · IGCSE Mathematics - International 0607

16 f(x) = 6cos(6x) Find the amplitude and the period of f(x). Amplitude = … Period = … [2] Questions 17 and 18 are printed on the next page.

2 marks

Mark scheme: 16 [amplitude = ] 6 2 B1 for each [period = ] 60 If 0 scored, SC1 if answers reversed

This question in 0607/23 May/June 2017

12 (a) On the grid, sketch the graph of y = sin x° for 0 G x G 360 . y x 0 360 [2] (b) The point (a, 0.5) is on the graph of y = sin x° . Find the two possible values of a. a = … or a = … [2]

4 marks

Mark scheme: 12(a) Correct Sketch 2 B1 for zeros at approx 0, 180, 360 B1 for max at approx (90, 1) and min at approx 2 y f(x)=sin (3.1416x/180) (270, –1) x 360 2 12(b) 30, 150 2 B1 for each

This question in 0607/23 May/June 2018

15 f (x) = 3 sin 2x° (a) Write down the amplitude of the graph of f ()x . … [1] (b) The graph of y = f ( x) goes through the points (75, 1.5) and (a, 1.5) . Find a possible value of a, greater than 75. … [1]

2 marks

Mark scheme: 15(a) 3 1 15(b) 195 or 255 or 375 or 435 etc. 1

This question in 0607/22 Oct/Nov 2018

12 sin i =- and 0° G i G 360° . 2 Find the two values of i. i = … or i = … [2]

2 marks

Mark scheme: 12 225, 315 2 B1 for each If 0 scored, M1 for 45 seen

This question in 0607/23 Oct/Nov 2018

11 The table shows some trigonometric ratios, each correct to 3 decimal places. Sine Cosine Tangent 40° 0.643 0.766 0.839 70° 0.940 0.342 2.747 Use this information to find (a) sin110°, … [1] (b) tan320°. … [1]

2 marks

Mark scheme: 11(a) 0.940 1 11(b) –0.839 1

This question in 0607/23 May/June 2020

16 a is acute and tan a = x . Find, in terms of x, (a) tan ( 180 - a) , tan ( 180 - a) = … [1] (b) tan ( 90 - a) . tan ( 90 - a) = … [1] Question 17 is printed on the next page.

2 marks

Mark scheme: 16(a) –x 1 16(b) 1 1 x

This question in 0607/23 Oct/Nov 2020

14 NOT TO SCALE k 3 cm 30° 12 cm Find the value of k. k = … [3] Questions 15 and 16 are printed on the next page.

3 marks

Mark scheme: 14 4 3 k 3 M1 for = tan 30 12 1 B1 for tan 30 = soi 3

This question in 0607/22 May/June 2021

20 tanx = k 0° 1 x 1 90° Find, in terms of k, (a) tan ( 180° - x) , … [1] (b) tan ( 90° - x) . … [1]

2 marks

Mark scheme: 20(a) –k 1 20(b) 1 1 k

This question in 0607/22 Oct/Nov 2021

10 60° NOT TO 2 3cm SCALE x cm Find the value of x. x = … [3]

3 marks

Mark scheme: 10 6 3 x M1 for tan 60 = 2 3 B1 for tan 60 = 3

This question in 0607/22 Oct/Nov 2022

15 f (x) 3 2 1 0 x 90 180 270 360 – 1 – 2 – 3 The graph shows f ( x) = a cos ( bx)°. (a) Find the value of a and the value of b. a = … b = … [2] (b) Write down the period of f ( )x . … [1] Question 16 is printed on the next page.

3 marks

Mark scheme: 15(a) a = 3 2 B1 for each b = 2 15(b) 180 1

This question in 0607/22 Oct/Nov 2023

17 cosx =- and 0° G x G 360° . 2 Find the values of x. x = … or x = … [2]

2 marks

Mark scheme: 17 150 2 B1 for each 210 If 0 scored SC1 for 30 seen

This question in 0607/22 Oct/Nov 2024

23 (a) f (x) 3 0 90 180 270 360 x – 3 The diagram shows the graph of f ( x°) = a cos bx . Find the value of a and the value of b. a = … b = … [2] 3 (b) Solve - 1 = 0 for values of x between 0° and 360°. tanx … [3]

5 marks

Mark scheme: 23(a) a = 3 2 B1 for each b = 2 23(b) 60, 240 only 3 B2 for 60 highlighted or M1 for tan x = 3 If 0 scored SC1 for their two answers (inside the range), which have a difference of 180

This question in 0607/22 Feb/March 2025

20 (a) Solve tanx = 3 for values of x between 0° and 360°. … [2] (b) This is a sketch of the graph of y = sin x . y 1 0 360° x – 1 Solve 4 sinx + 3 = 1 for values of x between 0° and 360°. … [3]

5 marks

Mark scheme: 20(a) 60, 240 cao 2 B1 for 1 correct and no extras in range or for 2 correct and one extra in range If 0 scored SC1 for answers k and k +180 or for tan60 and tan240 as final answer 20(b) 210, 330 only 3 B2 for 1 correct and no extras in range or for 2 correct and one extra in range or B1 for 1 correct and 1 incorrect in range OR 1 M1 for sinx = − 2 M1 for two answers adding to 180 or 540 If 0 scored SC1 for 30, 150, 210, 330

This question in 0607/21 May/June 2025

14 f ( x) = cos x , 0° G x G 360° (a) Write down the exact value of (i) f ( 0 ) … [1] (ii) f ( 30 ) . … [1] (b) y 1 0 x 360° -1 On the diagram, sketch the graph of y = f ( x) for 0° G x G 360° . [2] (c) Write down the amplitude of f ( )x . … [1]

5 marks

Mark scheme: 14(a)(i) 1 1 14(a)(ii) 3 1 2 14(b) Correct sketch 2 B1 for correct shape but wrong amplitude or period 14(c) 1 1

This question in 0607/23 May/June 2025

21 F NOT TO SCALE D C E 12 cm 3 cm A 4 cm B The diagram shows a triangular prism. The cross-section is a right-angled triangle EAB. AE = 3 cm, AB = 4 cm and BC = 12 cm. (a) Work out the length of BF. BF = … cm [3] (b) Find the sine of the angle between BF and the base ABCD. … [1]

4 marks

Mark scheme: 21(a) 13 3 M2 for 32 + 4 2 + 12 2 oe or M1 for 32 + 42 or 12 2 + 32 or 42 + 122 21(b) 3 1 13

This question in 0607/23 May/June 2025