All Obtained Different Results? Who's Right?
Geometry
Level
3
Students Michaelle, Maeve, Barbara and Antony, are asked to solve the equation \(2\sin x +\cos x -1=0\). Who solved it correctly?
- Michaelle found as the solution set \(\\\displaystyle S=\left \{ 2k\pi ,\,\arccos\left ( -\frac{3}{5} \right )+2k\pi \right \}\)
- Maeve found \(\\\displaystyle S=\left \{ 2k\pi ,\pi-\arcsin \frac{4}{5} +2k\pi \right \}\)
- Barbara found \(\\\displaystyle S=\left \{ 2k\pi ,2\arctan2 +2k\pi \right \}\)
- Antony found \(\\\displaystyle S=\left \{ 2k\pi ,\pi - 2\arcsin\frac{\sqrt{5}}{5} +2k\pi \right \}\)
by
Ervin Tronati