Let's solve the given problem step-by-step.
We have the equation [tex]\( y = -\cos(x) \)[/tex] and we are given that [tex]\( y = 1 \)[/tex]. We need to find the corresponding [tex]\( x \)[/tex] value between [tex]\( 0 \)[/tex] and [tex]\( 2\pi \)[/tex].
1. Set up the equation:
Start by substituting [tex]\( y = 1 \)[/tex] into the equation:
[tex]\[
1 = -\cos(x)
\][/tex]
2. Solve for [tex]\(\cos(x)\)[/tex]:
Rearrange the equation to solve for [tex]\(\cos(x)\)[/tex]:
[tex]\[
\cos(x) = -1
\][/tex]
3. Determine the [tex]\( x \)[/tex] value:
We need to find the values of [tex]\( x \)[/tex] between [tex]\( 0 \)[/tex] and [tex]\( 2\pi \)[/tex] where [tex]\( \cos(x) = -1 \)[/tex].
The value of [tex]\( \cos(x) \)[/tex] equals -1 at [tex]\( x = \pi \)[/tex] within the given interval. Therefore, the solution is:
[tex]\[
x = \pi
\][/tex]
So, the [tex]\( x \)[/tex] value that corresponds to [tex]\( y = 1 \)[/tex] between [tex]\( 0 \)[/tex] and [tex]\( 2\pi \)[/tex] is:
[tex]\[
\boxed{\pi}
\][/tex]
