Trigonometric ratios, sine and cosine rules and areaEdexcel A-Level Maths: Subtopic test

1. 1
   A point $P$ lies on the unit circle centred at the origin $O$. The angle from the positive $x$-axis to $OP$, measured anticlockwise, is $150^\circ$.

   (a)

   What is the $x$-coordinate of $P$?

   [1 mark]

   • A$\frac{\sqrt3}{2}$
   • B$-\frac{\sqrt3}{2}$
   • C$-\frac12$
   • D$\frac12$

   (b)

   What is the value of $\tan150^\circ$?

   [1 mark]

   • A$-\frac{1}{\sqrt3}$
   • B$\frac{1}{\sqrt3}$
   • C$-\sqrt3$
   • D$\sqrt3$

   (c)

   The point $Q$ on the unit circle corresponds to an angle of $210^\circ$. Write down the exact coordinates of $Q$.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   In triangle $ABC$, $AB=6$ cm, $BC=10$ cm and $A\hat{B}C=60^\circ$.

   (a)

   Find the length of $AC$.

   [1 mark]

   • A$14$ cm
   • B$76$ cm
   • C$\sqrt{136}$ cm
   • D$\sqrt{76}$ cm

   (b)

   Find the area of triangle $ABC$.

   [1 mark]

   • A$30\sqrt3$ cm$^2$
   • B$15$ cm$^2$
   • C$15\sqrt3$ cm$^2$
   • D$30$ cm$^2$

   (c)

   Find the size of angle $B\hat{A}C$, giving your answer to one decimal place.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   The angle $\theta$ satisfies $\sin\theta=\frac35$ and $90^\circ<\theta<180^\circ$. A triangle has two sides of lengths $10$ cm and $13$ cm with included angle $\theta$.

   (a)

   Find the exact values of $\cos\theta$ and $\tan\theta$.

   [3 marks]

   (b)

   Find the area of the triangle and the length of its third side.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   In triangle $ABC$, $AB=10$ cm, $BC=7$ cm and $B\hat{A}C=40^\circ$.

   (a)

   Show that there are two possible sizes for angle $A\hat{C}B$, and find both, to one decimal place.

   [6 marks]

   (b)

   Find the area of each of the two possible triangles, and the difference between the two areas.

   [6 marks]

   Total for question 4: 12 marks

End of questions