EDEXCEL GCSE MATHS · HIGHER
Exam Practice: Graph of the cosine function
Graph of the cosine function · More trigonometry · Lesson 3 of 9 · 15 marks · 25 minutes
|
Name |
|
Date |
|
Instructions
• Answer all the questions.
• Write your answers in the spaces provided.
• The marks for each question are shown in brackets - use this as a guide to how much to write.
• The answers are on separate pages at the back. Attempt every question before you look at them.
• Answer all questions. Show your working.
Question 1 SOLVE (3 marks)
Solve cos x = 0.3 for 0° ≤ x ≤ 360°. Give your answers correct to 1 decimal place.
|
|
|
|
|
|
|
|
(Total for Question 1 = 3 marks)
Question 2 WRITE DOWN (2 marks)
Write down the value of (a) cos 0° (b) cos 180°
|
|
|
|
|
|
(Total for Question 2 = 2 marks)
Question 3 USE THE GRAPH (3 marks)
The graph shows y = cos x for 0° ≤ x ≤ 360°. Use the graph to solve cos x = −0.5 and to write down the minimum value of cos x.
|
|
|
|
|
|
|
|
(Total for Question 3 = 3 marks)
Question 4 SOLVE (3 marks)
Solve cos x = −0.7 for 0° ≤ x ≤ 360°. Give your answers correct to 1 decimal place.
|
|
|
|
|
|
|
|
(Total for Question 4 = 3 marks)
Question 5 WRITE DOWN (2 marks)
cos 50°= 0.64 (to 2 decimal places). Write down another angle between 0° and 360° with cosine 0.64.
|
|
|
|
|
|
(Total for Question 5 = 2 marks)
Question 6 DESCRIBE (2 marks)
Describe the single transformation that maps the graph of y = sin x onto the graph of y = cos x.
|
|
|
|
|
|
(Total for Question 6 = 2 marks)
TOTAL FOR PAPER = 15 MARKS
|
|
Answers and mark scheme
Check your answer only once you have written one.
Question 1 (3 marks)
x = 72.5° and x = 287.5°
• cos ⁻¹(0.3) = 72.5° B1
• 360 − 72.5 M1
• 287.5 A1
Question 2 (2 marks)
(a) 1 (b) −1
• 1 B1
• −1 B1
Question 3 (3 marks)
x = 120° and x = 240°; minimum value −1.
• 120 B1
• 240 B1
• −1 B1
Question 4 (3 marks)
x = 134.4° and x = 225.6°
• cos ⁻¹(−0.7) = 134.4° B1
• 360 − 134.4 M1
• 225.6 A1
Question 5 (2 marks)
310°
• 360 − 50 M1
• 310 A1
Question 6 (2 marks)
A translation of 90° to the left.
• Translation M1
• 90° to the left A1