sine equation on an interval

Practise sine equation on an interval with an original VectorPaths question, worked explanation and related VCE Methods practice.

3 practice marks

Original practice question

Solve $\sin(2x)=\frac12$ for $0\leq x\leq2\pi$. Give all exact solutions.

Worked explanation

• Find the reference angle

  $\sin(\pi/6)=1/2$; sine is positive in quadrants I and II.

• Include every period

  List angles $2x=\pi/6+2k\pi$ and $2x=5\pi/6+2k\pi$ within $[0,4\pi]$.

• Divide and restrict

  $x\in\{\frac{\pi}{12},\frac{5 \pi}{12},\frac{13 \pi}{12},\frac{17 \pi}{12}\}$.

$x\in\{\frac{\pi}{12},\frac{5 \pi}{12},\frac{13 \pi}{12},\frac{17 \pi}{12}\}$.

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