График функции \(f\left( x \right) = a\sin x + b\) проходит через точки \(\left( {0;\frac{1}{2}} \right)\) и \(\left( {\frac{\pi }{2};3} \right)\). Следовательно:
\(\left\{ {\begin{array}{*{20}{c}}{\frac{1}{2} = a\sin 0 + b}\\{3 = a\sin \frac{\pi }{2} + b}\end{array}\,\,\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,\,\left\{ {\begin{array}{*{20}{c}}{\frac{1}{2} = a \cdot 0 + b}\\{3 = a \cdot 1 + b}\end{array}\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left\{ {\begin{array}{*{20}{c}}{b = \frac{1}{2}\,\,\,\,\,\,\,}\\{a + b = 3}\end{array}} \right.} \right.} \right.\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,a = \frac{5}{2}.\)
Ответ: 2,5.
Задача 9. На рисунке изображён график функции \(f\left( x \right) = a\,\,\sin x + b.\) Найдите a.