Question
What is the maximum value of j(x)=-8/7 sin x? enter in simplest fraction form
Answers
GPT-4o mini
The function \( j(x) = -\frac{8}{7} \sin x \) is a sine function multiplied by a negative coefficient. The sine function, \( \sin x \), has a maximum value of 1.
To find the maximum value of \( j(x) \), we can substitute the maximum value of \( \sin x \) into the equation:
\[
j(x) = -\frac{8}{7} \cdot 1 = -\frac{8}{7}.
\]
The maximum value of \( j(x) \) occurs when \( \sin x \) equals 1, thus the maximum value of \( j(x) \) is
\[
-\frac{8}{7}.
\]
Therefore, the answer is
\[
\boxed{-\frac{8}{7}}.
\]
To find the maximum value of \( j(x) \), we can substitute the maximum value of \( \sin x \) into the equation:
\[
j(x) = -\frac{8}{7} \cdot 1 = -\frac{8}{7}.
\]
The maximum value of \( j(x) \) occurs when \( \sin x \) equals 1, thus the maximum value of \( j(x) \) is
\[
-\frac{8}{7}.
\]
Therefore, the answer is
\[
\boxed{-\frac{8}{7}}.
\]