Determine the angle on the unit circle that has coordinates
- \(\left(1, 0\right)\) (1 mark)
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- \(\left(-\dfrac{\sqrt{3}}{2}, -\dfrac{1}{2}\right)\) (2 marks)
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Show Worked Solution
a. \((1, 0)\ \Rightarrow\ \text{Coordinates are on the positive \(y\)-axis.}\)
\(\theta = 90^{\circ}\)
b. \(\text{Coordinates are in the 3rd quadrant.}\)
\(\tan \theta= \dfrac{\frac{1}{2}}{\frac{\sqrt{3}}{2}} = \dfrac{1}{2} \times \dfrac{2}{\sqrt{3}} = \dfrac{1}{\sqrt{3}}\)
\(\text{Find reference angle:}\)
\(\theta =\tan^{-1}\left( \dfrac{1}{\sqrt{3}} \right) = 30^{\circ}\)
\(\text{Angle on unit circle}\ = 180+30=210^{\circ}\)