Respuesta :
To answer this question we will use the following properties of cosine:
1)
[tex]\cos \theta=\cos (360º-\theta)\text{.}[/tex]2)
[tex]\cos \theta=\cos (\theta+n\cdot360º)\text{.}[/tex]Now, applying arccosine to the given equation we get:
[tex]\begin{gathered} \cos ^{-1}(\cos x)=\cos ^{-1}0.341, \\ x\approx70.06218º. \end{gathered}[/tex]Using the first property we get that:
[tex]360º-70.06218º=289.93782º[/tex]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:
[tex]\begin{gathered} x=70.06218º+n\cdot360º\text{ or }x=289.93782º+n\cdot360º, \\ \text{where n is an integer.} \end{gathered}[/tex]Answer:
[tex]\begin{gathered} x=70.06218º+n\cdot360º\text{ or }x=289.93782º+n\cdot360º, \\ \text{where n is an integer.} \end{gathered}[/tex]
