Respuesta :

LammettHash
Assuming the function is

[tex]y=-2+5\sin\left(\dfrac\pi{12}(x-2)\right)[/tex]

recall that [tex]-1\le\sin x\le1[/tex], which means

[tex]-1\le\sin\left(\dfrac\pi{12}(x-2)\right)\le1[/tex]
[tex]\implies-5\le5\sin\left(\dfrac\pi{12}(x-2)\right)\le5[/tex]
[tex]\implies-7\le-2+5\sin\left(\dfrac\pi{12}(x-2)\right)\le3[/tex]

and so the minimum value is -7.
lublana

Answer:

-7

Step-by-step explanation:

We are given that   a function

[tex]y=-2+5 sin(\frac{\pi}{12}(x-2))[/tex]

We have to find the minimum value of y.

We know that range of sin x is [-1,1].

[tex]-1\leq sin(\frac{\pi}{12}(x-2))\leq 1[/tex]

[tex]-5\leq 5sin(\frac{\pi}{12}(x-2))\leq 5[/tex]

[tex]-5-2\leq -2+5sin(\frac{\pi}{12}(x-2))\leq 5-2[/tex]

[tex]-7\leq -2+5sin(\frac{\pi}{12}(x-2))\leq 3[/tex]

[tex]-7\leq y\leq 3[/tex]

Maximum value of y=3

Minimum value of y=-7

Hence, the minimum value of given function =-7

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