Solve the following equation for \( \beta \) over the interval \( [0,2 \pi) \), giving exact answers in radian units. If an equation has no solution, enter DNE. Multiple solutions should be entered as a comma-separated list. \( \sin (\beta)-\cos (2 \beta)=0 \) \( \beta=\square \)

In \( \triangle \mathrm{IJK}, k=1.9 \) inches, \( m \angle \mathrm{~J}=59^{\circ} \) and \( m \angle \mathrm{~K}=18^{\circ} \). Find the length of \( j \), to the nearest 10 th of an inch.

In \( \triangle X Y Z, x=410 \) inches, \( y=450 \) inches and \( z=210 \) inches. Find the measure of \( \angle X \) to the nearest degree.

In \( \triangle \mathrm{NOP}, n=54 \) inches, \( o=97 \) inches and \( p=95 \) inches. Find the measure of \( \angle \mathrm{N} \) to the nearest degree.

In \( \triangle \mathrm{PQR}, p=4.7 \) inches, \( m \angle \mathrm{P}=76^{\circ} \) and \( m \angle \mathrm{Q}=57^{\circ} \). Find the length of \( q \), to the nearest 10th of an inch.

(c) \( \sin (\pi+x)+\cos \left(\frac{\pi}{2}-x\right)+\tan \left(\frac{\pi}{2}+x\right)+\tan \left(\frac{3 \pi}{2}-x\right) \)