solve \\( \\cos ( x ) = 0.47 \\) on \\( 0 \\leq x < 2 \\pi \\).\nthere are two solutions, \\( a \\) and \\(…

Explanation:

Step1: Find the principal solution

We know that if (\cos(x) = a), then (x=\cos^{- 1}(a)+2k\pi) or (x = 2\pi-\cos^{-1}(a)+2k\pi), (k\in\mathbb{Z}). For (a = 0.47), the principal solution is (x_1=\cos^{-1}(0.47)). Using a calculator, (\cos^{-1}(0.47)\approx1.087) (in radians).

Step2: Find the second - solution

The second solution in the interval (0\leq x<2\pi) is (x_2 = 2\pi-\cos^{-1}(0.47)). (x_2=2\pi - 1.087\approx6.283 - 1.087=5.196)

Answer:

(A\approx1.087), (B\approx5.196)