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Advanced Trigonometry, SMB-015

Express each of the following in terms of its reference angle \(\theta\), where  \(0 \leq \theta \leq 90\).

  1. \(\sin 165^{\circ}\).   (1 mark)

  2. \(\cos 250^{\circ}\).   (1 mark)

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a.   \(\sin 15^{\circ}\)

b. \(-\cos 70^{\circ}\)

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a.   \(165^{\circ}\ \ \Rightarrow\ \ \text{2nd quadrant (sin +ve)} \)

\(\text{Reference angle:}\ \ 180-165=15^{\circ}\)

\(\sin 165^{\circ} = \sin 15^{\circ}\)

  

b.   \(250^{\circ}\ \ \Rightarrow\ \ \text{3rd quadrant (cos –ve)} \)

\(\text{Reference angle:}\ \ 180+\theta=250^{\circ}\ \ \Rightarrow \ \theta=70^{\circ}\)

\(\cos 250^{\circ} = -\cos 70^{\circ}\)