Answer: A
Step-by-step explanation:
You have:
[tex]20cos(\frac{2\pi }{5} x)=10\sqrt{2}[/tex]
Begin by dividing both sides by 20 to get:
[tex]cos(\frac{2\pi }{5} x)=\frac{\sqrt{2} }{2}[/tex]
Take the arccosine of both sides to get:
[tex]arccos(cos(\frac{2\pi }{5} x))=arccos(\frac{\sqrt{2} }{2})[/tex]
[tex]\frac{2\pi }{5} x=arccos(\frac{\sqrt{2} }{2} )[/tex]
First of all, lets find the right side. Cosine of what gives sqrt 2 over 2? That would be pi/4, plus 2npi. Another solution would be 7pi/4, plus 2npi. We have:
[tex]\frac{2\pi }{5} x=\pi /4+2n\pi[/tex]
[tex]\frac{2\pi }{5} x=7\pi /4+2n\pi[/tex]
Isolate 'x' to get:
[tex]x=\frac{5}{2\pi } (\pi /4+2n\pi)=\frac{5}{8} +5n[/tex]
[tex]x=\frac{5}{2\pi } (7\pi /4+2n\pi)=\frac{35}{8} +5n[/tex]
