\( \sin 32^{\circ}=\cos x \)

Step 1 ：\( \sin 32^{\circ} = \cos x \)

Step 2 ：\( \cos (90^{\circ} - 32^{\circ}) = \cos x \)

Step 3 ：\( x = 90^{\circ} - 32^{\circ} \)

Step 4 ：\( x = 58^{\circ} \)