Advanced Trigonometry, SMB-018

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

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a. \(-\tan 5^{\circ}\)

b. \(-\cos 82^{\circ}\)

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a. \(175^{\circ}\ \ \Rightarrow\ \ \text{2nd quadrant (sin +ve/cos –ve)} \)

\(\text{Reference angle:}\ 180-175=5^{\circ}\)

\(\tan 175^{\circ} = \dfrac{\sin 5^{\circ}}{-\cos 5^{\circ}} = -\tan 5^{\circ}\)

b. \(262^{\circ}\ \ \Rightarrow\ \ \text{3rd quadrant (cos –ve)} \)

\(\text{Reference angle:}\ \ 180+\theta=262^{\circ}\ \ \Rightarrow\ \ \theta=82^{\circ}\)

\(\cos 262^{\circ} = -\cos 82^{\circ}\)