Advanced Trigonometry, SMB-008

Determine the reference angle for \(315^{\circ}\). (1 mark)

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Using part (a) or otherwise, give the exact value for \(\sin 315^{\circ}\). (2 marks)

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a. \(45^{\circ}\)

b. \(-\dfrac{1}{\sqrt{2}}\)

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a. \(315^{\circ}\ \text{is in the 4th quadrant.}\)

\(\text{Reference angle:}\ \ 360-315=45^{\circ}\)

b. \(\sin 45^{\circ} = \dfrac{1}{\sqrt{2}}\)

\(\Rightarrow \ \sin \theta<0\ \ \text{in 4th quadrant}\)

\(\therefore \sin 315^{\circ} = -\dfrac{1}{\sqrt{2}}\)