Question

Solve for x in [0,360) cos2x= -0.123

Answer 1

Write out the equation given

`\cos 2x=-0.123`

Solving for x as shown below

`\begin{gathered} \cos 2x=-0.123 \\ 2x=\cos ^(-1)(-0.123) \\ 2x=-(82.93^0) \end{gathered}`

Note that cosine is always negative in the second and third quadrant

The value of 2x in the second quadrant would be

`\begin{gathered} 2x\text{ in the second quadrant is} \\ 2x=180^0-82.93^0 \\ 2x=97.07 \\ x=(97.07)/(2) \\ x=48.535^0 \end{gathered}`

The value of 2x in the third quadrant would be

`\begin{gathered} 2x\text{ in the third quadrant is} \\ 2x=180^0+82.93^0 \\ 2x=262.93 \end{gathered}`
`\begin{gathered} 2x=262.93 \\ x=(262.93)/(2) \\ x=131.465^0 \end{gathered}`

Hence, the values of x are 48.535° and 131.465°