Advanced Trigonometry, SMB-016

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

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a. \(\tan 55^{\circ}\)

b. \(-\sin 50^{\circ}\)

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a. \(235^{\circ}\ \ \Rightarrow\ \ \text{3rd quadrant (sin/cos –ve)} \)

\(\text{Reference angle:}\ 180+\theta=235^{\circ}\ \ \Rightarrow \ \theta=55^{\circ}\)

\(\tan 235^{\circ} = \dfrac{-\sin 55^{\circ}}{-\cos 55^{\circ}} = \tan 55^{\circ}\)

b. \(310^{\circ}\ \ \Rightarrow\ \ \text{4th quadrant (sin –ve)} \)

\(\text{Reference angle:}\ \ 360-310=50^{\circ}\)

\(\sin 310^{\circ} = -\sin 50^{\circ}\)