Find all solutions to the equation. \[ \cos 2 x+\sqrt{2} \cos x=-1 \] Write your answer in radians in terms of \( \pi \), and use the "or" button as necessary. Example: \( x=\frac{\pi}{5}+2 k \pi, k \in \mathbb{Z} \) or \( x=\frac{\pi}{7}+k \pi, k \in \mathbb{Z} \) \( x= \)

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.

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 \( 6 \cos (2 t)=6 \cos ^{2}(t)-2 \) 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 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 \( c \).

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.