(Solved): Example 5: Find one positive and one negative coterminal angles for each of the following angles a) ...

Example 5: Find one positive and one negative coterminal angles for each of the following angles a) \( 53^{\circ}: \) Positive \( = \) b) \( -\frac{\pi}{5}: \) Positive \( = \) Negative \( = \) Negative \( = \) Example 6: Find the reference angle \( \theta_{r} \) for each of the following angles: Note: If angle is more than one revolution, find the coterminal angle first. (a) \( \theta=\frac{\pi}{5} \) (d) \( \theta=290^{\circ} \) (b) \( \theta=-70^{\circ} \) (e) \( \theta=\frac{-5 \pi}{6} \) (c) \( \theta=\frac{2 \pi}{3} \) (f) \( \theta=910^{\circ} \) Example 7: Find the exact value of each of the following trigonometric functions using their reference angles. Do not use calculator Note: If angle is more than one revolution, find the coterminal angle first. a) \( \sin 135^{\circ} \) b) \( \cos 600^{\circ} \) c) For any acute angle \( \theta \), if \( \sin \theta=\frac{1}{5}, f i \) i) \( \csc (4 \pi-\theta) \) ii) \( \cos (\pi+\theta) \) d) Given \( \cos \alpha=A \) and \( \sin \alpha=B \) and \( \alpha \) is a reference angle. Write below expression in terms of \( \boldsymbol{A} \) and \( \boldsymbol{B} \) and express your answer in simplest form. \[ \cos (3 \pi+\alpha)+\tan \left(\frac{\pi}{2}-\alpha\right) \]