Suppose that \( \alpha \) and \( \beta \) are angles given as follows: \( \sin \alpha=\frac{12}{13} \) and \( \alpha \) is an angle in quadrant 1. \( \cos \beta=-\frac{4}{5} \) and \( \beta \) is an angle in quadrant 2. Compute the exact value of \( \sin (\alpha+\beta) \)

(1) จงหาค่าของ \( 2 \sin 20^{\circ}+\cot 68^{\circ} \)

When evaluating the expression \( \tan ^{-1}\left(-\frac{\sqrt{3}}{3}\right) \), the angle obtained is ...

NIVEL: INTERMEDIO 3) En un trángulo rectángulo, siendo " \( \alpha \) " un ángulo agudo se cumple que sen \( \alpha=\frac{5}{13} \) Calcular \( H=24 \) tana +3 . 4) Si tan \( \Phi=\frac{\sqrt{6}}{3} \), donde " \( \Phi \) " es un ángulo agudo, calcular

4) \( \operatorname{Si} \tan \Phi=\frac{\sqrt{6}}{3} \), donde \( \Phi \) ' es un ángulo agudo, calcular: \( P=\sqrt{3} \operatorname{Sec} \Phi+\sqrt{2} \operatorname{Csc} \Phi \)

Nite the expression below in surd form and rationalize the denominator \[ \frac{1-\cos 60^{\circ}}{1+\operatorname{tim} 30^{\circ}} \]