Solve \( 2 \sin (2 t)-1 \sin (t)=0 \) for all solutions \( 0 \leq t<2 \pi \) \( t=\square \)

If \( \theta=-\frac{2 \pi}{3} \), then find exact values for the following: \( \sin (\theta)=\square \) \( \cos (\theta)=\square \) \( \tan (\theta)=\square \) \( \csc (\theta)=\square \) \( \sec (\theta)=\square \) \( \cot (\theta)=\square \)

\( \frac { \sin A } { 1 + \cos A } + \frac { 1 - \operatorname { cosec } A } { \sin A } = 2 \operatorname { cosec } A \)

If \( \sin (\theta)=-\frac{2}{3} \), and \( \theta \) is in quadrant IV, then find (a) \( \cos (\theta)=\square \) (b) \( \tan (\theta)=\square \) (c) \( \sec (\theta)=\square \) (d) \( \csc (\theta)=\square \) (e) \( \cot (\theta)=\square \)

\begin{tabular}{l} (b) Using the formula \( \operatorname{Sin} 2 A=2 \operatorname{Sin} A \operatorname{Cos} A \) \\ solve the equation \( \sin 2 x-\cos x=0 \) \\ in the interval \( 0^{\circ} \leq x \leq 360^{\circ} \) \\ \hline\end{tabular}

\begin{tabular}{l} (b) Using the formula \( \operatorname{Sin} 2 A=2 \operatorname{Sin} A \operatorname{Cos} A \) \\ solve the equation \( \sin 2 x-\cos x=0 \) \\ in the interval \( 0^{\circ} \leq x \leq 360^{\circ} \) \\ \hline\end{tabular}