solve cos(x)= -0.58 on 0 ≤ x < 2π there are two solutions, a and b, with a < b

Explanation:

Step1: Use inverse - cosine function

$x=\cos^{-1}(- 0.58)$

Step2: Find the first solution in the second quadrant

$A=\pi-\cos^{-1}(0.58)$ Using a calculator, $\cos^{-1}(0.58)\approx0.94$ radians. So $A=\pi - 0.94\approx3.14 - 0.94 = 2.20$ radians.

Step3: Find the second solution in the third quadrant

$B=\pi+\cos^{-1}(0.58)$ $B=\pi + 0.94\approx3.14+0.94 = 4.08$ radians.

Answer:

$A\approx2.20$, $B\approx4.08$