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 \(\\\displaystyle S=\left \{ 2k\pi ,\pi - 2\arcsin\frac{\sqrt{5}}{5} +2k\pi \right \}\)

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