A point \(X\) is located on the unit circle at angle 300\(^{\circ}\) from the positive \(x\)-axis.
- Determine the quadrant in which \(X\) lies. (1 mark)
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- Find the coordinates of point \(X\). (2 marks)
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Show Worked Solution
a.
\(300^{\circ}\ \text{lies in Quadrant IV}\ \ (270^{\circ} \lt 300^{\circ} \lt 360^{\circ}) \)
b. \(\text{Reference angle}\ (\theta):\ 360^{\circ}-\theta=300^{\circ}\ \ \Rightarrow \ \ \theta=60^{\circ}\)
\(x\text{-coordinate of}\ X = \cos\,60^{\circ} = \dfrac{1}{2}\)
\(y\text{-coordinate of}\ X = -\sin\,60^{\circ} = -\dfrac{\sqrt{3}}{2}\)
\(X\left( \dfrac{1}{2}, -\dfrac{\sqrt{3}}{2}\right) \)