Trigonometric equation over two periods

Practise trigonometric equation over two periods with an original VectorPaths question, worked explanation and related VCE Methods practice.

4 practice marks

Original practice question

Consider $\sin(2x)=\sqrt3/2$ on $0\leq x\leq2\pi$. (a) State the interval for $2x$. [1 marks] (b) Find all exact values of x. [3 marks]

Worked explanation

• Part (a)

  Multiply both interval endpoints by 2; two full sine periods must be considered.

• Part (b)

  $2x=\pi/3,2\pi/3,7\pi/3,8\pi/3$. Dividing all four values by 2 gives the required solutions.

(a) $[0,4\pi]$.; (b) $\pi/6,\pi/3,7\pi/6,4\pi/3$.

Original VectorPaths practice; not an official VCAA question or marking rubric.