Question

Solve -6cos x - 12 = 0 on the interval [0, 2n).Ο 5π 7π66O No solutionΟ 2π 4π33Ο coς-1 (-2), Π - cos-1 (-2)

Answer 1

`-6\cos (x)-12=0`

Solve for x:

add 12 to both sides:

`\begin{gathered} -6\cos (x)-12+12=+12 \\ -6\cos (x)=12 \end{gathered}`

divide both sides by -6:

`\begin{gathered} (-6\cos (x))/(-6)=(12)/(-6) \\ \cos (x)=-2 \end{gathered}`

Take the inverse cosine of both sides:

`\begin{gathered} x=2\pi n1+\cos ^(-1)(-2) \\ or \\ x=2\pi n2-\cos ^(-1)(-2) \\ n1\in\Z \\ n2\in\Z \end{gathered}`