Using the Law of Sines to solve for all possible triangles if \( \angle B=43^{\circ}, a=109, b=42 \). If no answer exists, enter DNE for all answers. \( \angle A \) is \( \square \) degrees \( \angle C \) is \( \square \) degrees \( c=\square \) Assume \( \angle A \) is opposite side \( a, \angle B \) is opposite side \( b \), and \( \angle C \) is opposite side \( c \).

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) \( \cot (\theta)=\square \)

Without using a calculator, compute the sine and cosine of \( 120^{\circ} \) by using the reference angle. What is the reference angle? In what quadrant is this angle? \( \sin \left(120^{\circ}\right)=\square \) degrees. \( \cos \left(120^{\circ}\right)=\square \) (Type sqrt(2) for \( \sqrt{2} \) and sqrt(3) for \( \sqrt{3} \).)

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? \( \sin \left(\frac{3 \pi}{4}\right)=\square \) \( \cos \left(\frac{3 \pi}{4}\right)=\square \)

Find the exact values of the six trig functions. Give an exact answer. No decimals!!! \( \sin \left(300^{\circ}\right)=\square \) \( \cos \left(300^{\circ}\right)=\square \) \( \tan \left(300^{\circ}\right)=\square \) \( \csc \left(300^{\circ}\right)=\square \) \( \sec \left(300^{\circ}\right)=\square \) \( \cot \left(300^{\circ}\right)=\square \)

\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}