Advanced Trigonometry, SMB-017

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. \(-\cos 40^{\circ}\)

b. \(-\tan 15^{\circ}\)

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a. \(140^{\circ}\ \ \Rightarrow\ \ \text{2nd quadrant (cos –ve)} \)

\(\text{Reference angle:}\ \ 180-140=40^{\circ}\)

\(\cos 140^{\circ} = -\cos 40^{\circ}\)

b. \(345^{\circ}\ \ \Rightarrow\ \ \text{4th quadrant (sin –ve/cos +ve)} \)

\(\text{Reference angle:}\ 360-345=15^{\circ}\ \ \Rightarrow \ \theta=15^{\circ}\)

\(\tan 345^{\circ} = \dfrac{-\sin 15^{\circ}}{\cos 15^{\circ}} = -\tan 15^{\circ}\)