Question

If Cos x= 0.341, then X=?

Answer 1

To answer this question we will use the following properties of cosine:

1)

`\cos \theta=\cos (360º-\theta)\text{.}`

2)

`\cos \theta=\cos (\theta+n\cdot360º)\text{.}`

Now, applying arccosine to the given equation we get:

`\begin{gathered} \cos ^(-1)(\cos x)=\cos ^(-1)0.341, \\ x\approx70.06218º. \end{gathered}`

Using the first property we get that:

`360º-70.06218º=289.93782º`

is also a solution to the given equation.

Finally, by the second property, we get that the solutions to the given equation are of the form:

`\begin{gathered} x=70.06218º+n\cdot360º\text{ or }x=289.93782º+n\cdot360º, \\ \text{where n is an integer.} \end{gathered}`

Answer:

`\begin{gathered} x=70.06218º+n\cdot360º\text{ or }x=289.93782º+n\cdot360º, \\ \text{where n is an integer.} \end{gathered}`