Question

Solve -12cos x + 6 = 0 on the interval [0, 2n).OT 5T3' 3T 273' 32427 4T3,T 1176' 6

Answer 1

n/3, 5n/3

Step-by-step explanation:

Given the equation:

`-12\cos x+6=0,\lbrack0,2\pi)`

Subtract 6 from both sides:

`\begin{gathered} -12\cos x+6-6=0-6 \\ -12\cos x=-6 \end{gathered}`

Next, divide both sides by -12:

`\begin{gathered} (-12\cos x)/(-12)=-(6)/(-12) \\ \cos x=0.5 \end{gathered}`

Finally, solve for x in the interval [0, 2n).

`\begin{gathered} x=\arccos (0.5) \\ x=(\pi)/(3) \\ x=2\pi-(\pi)/(3)=(5\pi)/(3) \end{gathered}`

The first choice is correct.