Solving trigonometric equationsAQA A-Level Maths: Subtopic test

1. 1
   In this question, $x$ is in degrees and $0^\circ\le x\le360^\circ$.

   (a)

   Solve $\tan x=-1$.

   [1 mark]

   • A$45^\circ,\ 225^\circ$
   • B$135^\circ,\ 225^\circ$
   • C$45^\circ,\ 315^\circ$
   • D$135^\circ,\ 315^\circ$

   (b)

   Solve $2\cos x+1=0$.

   [1 mark]

   • A$120^\circ,\ 240^\circ$
   • B$60^\circ,\ 300^\circ$
   • C$120^\circ,\ 300^\circ$
   • D$150^\circ,\ 210^\circ$

   (c)

   Solve $\sin x=-0.6$, giving your answers to 1 decimal place.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Consider the equation $2\sin^2\theta+\sin\theta-1=0$, where $\theta$ is in degrees.

   (a)

   Which is the factorised form of $2\sin^2\theta+\sin\theta-1$?

   [1 mark]

   • A$(2\sin\theta+1)(\sin\theta-1)$
   • B$(2\sin\theta-1)(\sin\theta-1)$
   • C$(2\sin\theta-1)(\sin\theta+1)$
   • D$(\sin\theta-2)(\sin\theta+1)$

   (b)

   How many solutions does the equation have for $0^\circ\le\theta\le720^\circ$?

   [1 mark]

   • A$3$
   • B$6$
   • C$4$
   • D$8$

   (c)

   Solve the equation for $0^\circ\le\theta\le360^\circ$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   In this question, $x$ is measured in degrees.

   (a)

   Solve $\sin2x=\frac{\sqrt3}{2}$ for $0^\circ\le x\le180^\circ$.

   [3 marks]

   (b)

   Solve $\cos(3x-30^\circ)=0.5$ for $0^\circ\le x\le180^\circ$.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   In this question, $x$ is in radians and $0\le x\le2\pi$.

   (a)

   Solve $2\sin^2x+5\cos x+1=0$, giving your answers in terms of $\pi$.

   [6 marks]

   (b)

   Solve $\tan x=3\sin x$, giving non-exact answers to 3 significant figures.

   [6 marks]

   Total for question 4: 12 marks

End of questions