Advanced Trigonometry, SMB-010

Determine the reference angle for \(210^{\circ}\). (1 mark)

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Using part (a) or otherwise, give the exact value for \(\tan 210^{\circ}\) (2 marks)

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a. \(30^{\circ}\)

b. \(\dfrac{1}{\sqrt{3}}\)

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a. \(210^{\circ}\ \text{is in the 3rd quadrant.}\)

\(\text{Reference angle:}\ \ 180+\theta=210^{\circ}\ \ \Rightarrow \ \ \theta = 30^{\circ}\)

b. \(\tan 30^{\circ} = \dfrac{1}{\sqrt{3}}\)

\(\Rightarrow \ \tan \theta>0\ \ \text{in 3rd quadrant}\)

\(\therefore \tan 210^{\circ} = \dfrac{1}{\sqrt{3}}\)