Question

For equation solve for x given 0

Answer 1

x=2.61 radians

Step-by-step explanation

`2\cos (x)+\sqrt[]{3}=0`

Step 1

Let's isolate x

a)

`\begin{gathered} 2\cos (x)+\sqrt[]{3}=0 \\ \text{subtract }\sqrt[]{3}\text{ in both sides} \\ 2\cos (x)+\sqrt[]{3}-\sqrt[]{3}=0-\sqrt[]{3} \\ 2\cos (x)=-\sqrt[]{3} \end{gathered}`

Step 2

b) now, divide both sides by 2

`\begin{gathered} 2\cos (x)=-\sqrt[]{3} \\ \text{divide both sides by 2} \\ (2\cos(x))/(2)=\frac{-\sqrt[]{3}}{2} \\ \cos (x)=\frac{-\sqrt[]{3}}{2} \\ \end{gathered}`

Step 3

c) finally,Inverse cosine in both sides ( remember we are looking for an angle)

`\begin{gathered} \cos (x)=\frac{-\sqrt[]{3}}{2} \\ \text{ Inverse cosine in both sides} \\ \cos ^(-1)(\cos (x))=\cos ^(-1)(\frac{-\sqrt[]{3}}{2}) \\ x=\cos ^(-1)(\frac{-\sqrt[]{3}}{2}) \\ x=\cos ^(-1)(-0.86) \\ x=2.61\text{ radians} \end{gathered}`

therefore, the answer is

x=2.61 radians

I hope this helps you