If \( \theta=-\frac{7 \pi}{4} \), then find exact values for the following: \( \sin (\theta)=\square \) \( \cos (\theta)=\square \) \( \tan (\theta)=\square \) \( \csc (\theta)=\square \)

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 \( c \).

Solve \( 6 \cos (2 t)=6 \cos ^{2}(t)-2 \) for all solutions \( 0 \leq t<2 \pi \). \( t=\square \) Give your answers accurate to at least 2 decimal places and in a list separated by commas.

Solve \( 4 \sin \left(\frac{\pi}{4} x\right)=2 \) for the four smallest positive solutions. \( x=\square \) Give your answers accurate to at least two decimal places, as a list separated by commas.

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

Solve \( 9 \cos (2 \alpha)=9 \sin ^{2}(\alpha)+4 \) for all solutions \( 0 \leq \alpha<2 \pi \). \( \alpha=\square \) Give your answers accurate to at least 2 decimal places and in a list separated by commas.