График функции \(f\left( x \right) = a\cos x + b\) проходит через точки \(\left( {0;3} \right)\) и \(\left( {\frac{\pi }{2};\frac{3}{2}} \right)\). Следовательно:
\(\left\{ {\begin{array}{*{20}{c}}{3 = a\cos 0 + b}\\{\frac{3}{2} = a\cos \frac{\pi }{2} + b}\end{array}} \right.\,\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,\,\left\{ {\begin{array}{*{20}{c}}{3 = a \cdot 1 + b}\\{\frac{3}{2} = a \cdot 0 + b}\end{array}} \right.\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,\left\{ {\begin{array}{*{20}{c}}{a + b = 3}\\{b = \frac{3}{2}\,\,\,\,\,}\end{array}} \right.\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,a = \frac{3}{2}.\)
Ответ: 1,5.
Задача 2. На рисунке изображён график функции \(f\left( x \right) = a\,\,\cos x + b.\) Найдите a.