Question

For the function y=-2+5sin(pi/12)(x-2)), what is the minimum value

Answer 1

Assuming the function is


`y=-2+5\sin\left(\frac\pi{12}(x-2)\right)`

recall that
`-1\le\sin x\le1`, which means


`-1\le\sin\left(\frac\pi{12}(x-2)\right)\le1`

`\implies-5\le5\sin\left(\frac\pi{12}(x-2)\right)\le5`

`\implies-7\le-2+5\sin\left(\frac\pi{12}(x-2)\right)\le3`

and so the minimum value is -7.

Answer 2

-7

Explanation:

We are given that a function

`y=-2+5 sin((\pi)/(12)(x-2))`

We have to find the minimum value of y.

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

`-1\leq sin((\pi)/(12)(x-2))\leq 1`

`-5\leq 5sin((\pi)/(12)(x-2))\leq 5`

`-5-2\leq -2+5sin((\pi)/(12)(x-2))\leq 5-2`

`-7\leq -2+5sin((\pi)/(12)(x-2))\leq 3`

`-7\leq y\leq 3`

Maximum value of y=3

Minimum value of y=-7

Hence, the minimum value of given function =-7