Solving trigonometric equationsEdexcel A-Level Maths: Subtopic test

1. 1
   The equation $\sin(x+70^\circ)=0.5$ is to be solved for $0<x<360^\circ$.

   (a)

   A calculator gives $\sin^{-1}0.5=30^\circ$. What is the other value of $x+70^\circ$ between $0^\circ$ and $360^\circ$?

   [1 mark]

   • A$150^\circ$
   • B$330^\circ$
   • C$210^\circ$
   • D$120^\circ$

   (b)

   Which pair gives all the solutions for $x$?

   [1 mark]

   • A$-40^\circ$ and $80^\circ$
   • B$30^\circ$ and $150^\circ$
   • C$80^\circ$ and $330^\circ$
   • D$80^\circ$ and $320^\circ$

   (c)

   Solve $\sin(x+70^\circ)=-0.5$ for $0<x<360^\circ$.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   The equation $3+5\cos2x=1$ is to be solved for $-180^\circ<x<180^\circ$.

   (a)

   Which is the correct rearrangement of the equation?

   [1 mark]

   • A$\cos2x=\frac25$
   • B$\cos2x=-\frac25$
   • C$\cos2x=-2$
   • D$\cos x=-\frac15$

   (b)

   Which interval must be used when solving for $2x$?

   [1 mark]

   • A$-180^\circ<2x<180^\circ$
   • B$0^\circ<2x<360^\circ$
   • C$-360^\circ<2x<360^\circ$
   • D$-90^\circ<2x<90^\circ$

   (c)

   Solve the equation, giving your answers to 1 decimal place.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Consider the equation $6\cos^2x+\sin x-5=0$ for $0\le x<360^\circ$.

   (a)

   Show that the equation can be written as $6\sin^2x-\sin x-1=0$.

   [3 marks]

   (b)

   Hence solve the equation for $0\le x<360^\circ$, giving answers to 1 decimal place where necessary.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   In this question $x$ is measured in radians with $0\le x<2\pi$, and answers should be given as exact multiples of $\pi$.

   (a)

   Solve $2\cos^2x=3-3\sin x$.

   [6 marks]

   (b)

   Solve $\sin3x=\frac{\sqrt3}{2}$.

   [6 marks]

   Total for question 4: 12 marks

End of questions