A point \(Q\) is located on the unit circle at angle 150\(^{\circ}\) from the positive \(x\)-axis.
- Determine the quadrant in which \(Q\) lies. (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
- Find the coordinates of point \(Q\). (2 marks)
--- 6 WORK AREA LINES (style=lined) ---
Show Worked Solution
a. \(150^{\circ}\ \text{lies in Quadrant II}\ \ \ (90^{\circ} \lt 150^{\circ} \lt 180^{\circ})\)
b.
\(x\text{-coordinate}\ = -\cos\,30^{\circ} = -\dfrac{\sqrt{3}}{2}\)
\(y\text{-coordinate}\ = \sin\,30^{\circ} = \dfrac{1}{2}\)
\(Q\left( -\dfrac{\sqrt{3}}{2}, \dfrac{1}{2}\right) \)