(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.