Work out the exact value of sin 30 degrees plus cos 60 degrees.
(Total for Question 6 is 2 marks)
7
Work out the exact value of tan 30 degrees. Give your answer in a simplified exact form.
(Total for Question 7 is 2 marks)
8
Work out the exact value of cos 30 degrees minus sin 60 degrees.
(Total for Question 8 is 2 marks)
9
A right-angled triangle has hypotenuse length 10 cm and one acute angle 30 degrees. Work out the exact length of the side opposite the 30 degree angle.
(Total for Question 9 is 2 marks)
10
Show that sin 45 degrees multiplied by √2 equals 1. You must show the steps.
(Total for Question 10 is 2 marks)
Mark scheme · 5.20F Exact trig values: Foundation Tier Practice
Question 1
B1 1/2 cao
Answer: 1/2
Question 2
B1 1/2 cao
Answer: 1/2
Question 3
B1 1 cao
Answer: 1
Question 4
B1√2/2 cao
Answer: √2/2
Question 5
B1√2/2 cao
Answer: √2/2
Question 6
M1 correct substitution of sin 30 = 1/2 and cos 60 = 1/2 or equivalent method
A1 1 cao
Answer: 1
Question 7
M1 use sin 30 and cos 30 or the known exact ratio tan 30 = 1/√3
A1√3/3 cao (rationalised form)
Answer: √3/3
Question 8
M1 substitute cos 30 = √3/2 and sin 60 = √3/2 or equivalent method
A1 0 cao
Answer: 0
Question 9
M1 use sin 30 = opposite/hypotenuse to form opposite = 10 * sin 30
A1 5 cm cao
Answer: 5 cm
Question 10
M1 substitute sin 45 = √2/2 and multiply by √2 or equivalent method