Find the exact values of the six trig functions. Give an exact answer. No decimals!!! \( \begin{array}{l}\sin \left(225^{\circ}\right)=\frac{\sqrt{2}}{2} \\ \cos \left(225^{\circ}\right)=\frac{\sqrt{2}}{2} \\ \tan \left(225^{\circ}\right)=\square \\ \csc \left(225^{\circ}\right)=\square \\ \sec \left(225^{\circ}\right)=\square \\ \cot \left(225^{\circ}\right)=\square\end{array} \)

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.

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 \( c \).

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 \( c \).

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.

Using the Law of Sines to solve the triangle if \( \angle A=111^{\circ}, a=34, b=14 \). If no answer exists, enter DNE for all answers. \( \angle B \) is 22.6 \( \angle C \) is 46.4 \( c= \) Assume \( \angle A \) is opposite side \( a, \angle B \) is opposite side \( b \), and \( \angle C \) is opposite side \( c \).