(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.