If \( \theta=-\frac{5 \pi}{4} \), then find exact values for the following: \( \sin (\theta)=\frac{\sqrt{2}}{2} \) \( \cos (\theta)=-\frac{\sqrt{2}}{2} \) \( \tan (\theta)=-1 \) \( \csc (\theta)=-\sqrt{2} \)

Using the Law of Sines to solve the triangle if \( \angle A=37^{\circ}, \angle C=72^{\circ}, b=12: \) \( \angle B \) is 71 \( a=7.63 \) \( c=\square \) degrees; Round to two decimal places if needed. Assume \( \angle A \) is opposite side \( a, \angle B \) is opposite side \( b \), and \( \angle C \) is opposite side \( c \).

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 \( 9 \cos (2 \alpha)=9 \sin ^{2}(\alpha)+4 \) 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.

Solve \( 4 \cos (2 x)=4 \cos ^{2}(x)-1 \) for all solutions \( 0 \leq x<2 \pi \) \( x=\square \) Give your answers accurate to at least 2 decimal places and in a list separated by commas.

Using the Law of Sines to solve the triangle if \( \angle A=37^{\circ}, \angle C=72^{\circ}, b=12 \) : \( \angle B \) is \( \square \) degrees; \( a=\square=\square \) Round to two decimal places if needed. Assume \( \angle A \) is opposite side \( a, \angle B \) is opposite side \( b \), and \( \angle C \) is opposite side \( c \).