Answer: \(x=-1.24,\ -0.195,\ 0.852\) to three significant figures.

Answer: \(x=-1.24,\ -0.195,\ 0.852\) to three significant figures.

Let

\(u=3x+1.2.\)

The equation becomes

\(\sqrt2\cos u=2\sin u.\)

Divide by \(\cos u\):

\(\sqrt2=2\tan u.\)

Therefore

\(\tan u=\frac{1}{\sqrt2}.\)

Now

\(-1.5\leq x\leq1.5,\)

so

\(-3.3\leq u\leq5.7.\)

The principal value is

\(\arctan\frac1{\sqrt2}\approx0.615.\)

Within the interval \(-3.3\leq u\leq5.7\), the possible values are

\(u\approx -2.526,\quad 0.615,\quad 3.757.\)

Since \(u=3x+1.2\),

\(x=\frac{u-1.2}{3}.\)

This gives

\(x\approx -1.24,\quad -0.195,\quad 0.852.\)