Pure Mathematics (A Level) Unit Test 6: Trigonometry
1 Figure 1 shows a logo comprised of a rhombus surrounded by two arcs. Arc BAD
has centre C and arc BCD has centre A. Some of the dimensions of the logo are
shown in the diagram.
Figure 1
Prove that the shaded area of the logo is (8 marks)
2 a When θ is small, show that the equation can be written as
(4 marks)
b Hence write down the value of when θ is small. (1 mark)
3 a Prove that (3 marks)
b Hence solve, in the interval , the equation (3 marks)
4 Figure 2 shows the right-angled triangles and , with
and .
Figure 2
Prove that (8 marks)
© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 1
1 Figure 1 shows a logo comprised of a rhombus surrounded by two arcs. Arc BAD
has centre C and arc BCD has centre A. Some of the dimensions of the logo are
shown in the diagram.
Figure 1
Prove that the shaded area of the logo is (8 marks)
2 a When θ is small, show that the equation can be written as
(4 marks)
b Hence write down the value of when θ is small. (1 mark)
3 a Prove that (3 marks)
b Hence solve, in the interval , the equation (3 marks)
4 Figure 2 shows the right-angled triangles and , with
and .
Figure 2
Prove that (8 marks)
© Pearson Education Ltd 2017. Copying permitted for purchasing institution only. This material is not copyright free. 1
