Solve for \( x \) in \( 2 \sin x \tan x+\tan x-2 \sqrt{3} \sin x-\sqrt{3}=0 \)

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

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} Resoluer el siguiente triangub. \\ \hline \( 5^{\circ} \) \\ \( \sin \alpha \)\end{tabular}\( \frac{B}{\operatorname{sen} \beta} \)

\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}

Without using a calculator, compute the sine and cosine of \( \frac{3 \pi}{4} \) by using the refer What is the reference angle? \( \square \) radians. In what quadrant is this angle? \( \sin \left(\frac{3 \pi}{4}\right)=\square \) \( \cos \left(\frac{3 \pi}{4}\right)=\square \)