Solving Trig Equations with Calculators, Part II — Question 10

Question 10 - Solution

Use

$$\sin x+\cos x=\sqrt2\sin(x+\pi/4).$$

Let $\alpha=\arcsin(1.2/\sqrt2)$. The two solution families are

$$x=\alpha-\pi/4+2k\pi,\qquad x=3\pi/4-\alpha+2k\pi.$$

Only $k=0$ gives values in $[0,2\pi]$, hence

$$\boxed{x\approx 0.23,\ 1.34}.$$

Both satisfy the unsquared equation; adding $\pi$ reverses the sign and does not give another solution.