**\#5.) Sahara says that \( -135^{\circ} \) is coterminal to \( 565^{\circ} \) since they end up in the same quadrant. Do you agree or disagree with her? Explain your reasoning and show work to support it.

I disagree with Sahara's statement. To determine if two angles are coterminal, we should check if the difference between them is a multiple of \(360^{\circ}\). First, we can find a coterminal angle for \(-135^{\circ}\) by adding \(360^{\circ}\): \[ -135^{\circ} + 360^{\circ} = 225^{\circ} \] Now, let's see if \(565^{\circ}\) can be reduced by subtracting \(360^{\circ}\): \[ 565^{\circ} - 360^{\circ} = 205^{\circ} \] Since \(225^{\circ}\) and \(205^{\circ}\) are not equal, \(-135^{\circ}\) and \(565^{\circ}\) are not coterminal. Additionally, let’s check the quadrant locations: - \(-135^{\circ}\) is in the second quadrant (as it goes clockwise) and \(565^{\circ}\) is in the first quadrant. Therefore, they do not even end up in the same quadrant, which reinforces that they are not coterminal.