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Determine the minimum and maximum value of the following trigonometric function.
f(x)=10sin(2/5x)+5

Determine The Minimum And Maximum Value Of The Following Trigonometric Functionfx10sin25x5 class=

Sagot :

ANSWER

[tex]\begin{gathered} Minimum=-5 \\ Maximum=15 \end{gathered}[/tex]

EXPLANATION

The trigonometric function given is:

[tex]f(x)=10\sin (\frac{2}{5}x)+5[/tex]

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

This means that the minimum value of the function is:

[tex]\begin{gathered} 10(-1)+5 \\ \Rightarrow-10+5 \\ \Rightarrow-5 \end{gathered}[/tex]

The maximum value a sine function can take is 1.

This means that the maximum value of the function is:

[tex]\begin{gathered} 10(1)+5 \\ \Rightarrow10+5 \\ \Rightarrow15 \end{gathered}[/tex]

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