Question

Determine the minimum and maximum value of the following trigonometric function.

f(x)=10sin(2/5x)+5

Answer 1

`\begin{gathered} Minimum=-5 \\ Maximum=15 \end{gathered}`

Step-by-step explanation

The trigonometric function given is:

`f(x)=10\sin ((2)/(5)x)+5`

The minimum value a sine function can take is -1.

This means that the minimum value of the function is:

`\begin{gathered} 10(-1)+5 \\ \Rightarrow-10+5 \\ \Rightarrow-5 \end{gathered}`

The maximum value a sine function can take is 1.

This means that the maximum value of the function is:

`\begin{gathered} 10(1)+5 \\ \Rightarrow10+5 \\ \Rightarrow15 \end{gathered}`