(a) If \(9 \cos x - 7 = 1\) and \(0° \leq x \leq 90°\), find x. (b) Given that x is an integer, find the three greatest values of x which satisfy the inequality \(7x < 2x - 13\).
Explanation
(a) \(9 \cos x - 7 = 1 \implies 9 \cos x = 1 + 7 = 8\) \(\cos x = \frac{8}{9}\) \(x = \cos^{-1} (0.8889)\) \(x = 27.26°\) (b) \(7x < 2x - 13\) \(7x - 2x < - 13\) \(5x < - 13\) \(x < \frac{-13}{5}\) \([-2.6] = -3, -4, -5\) Note : The greatest value function rounds up a real number to an integer that is less or equal to the real number.