Answer:
[tex]x=\frac{cos^{-1}(0.45)+2n\pi}{3} ,x=\frac{2\pi- cos^{-1}(0.45)+2n\pi}{3}[/tex]
Step-by-step explanation:
Given: [tex]2 cos(3x)=0.9[/tex]
To find: solutions of the given equation
Solution:
Triangle is a polygon that has three sides, three angles and three vertices.
Trigonometry explains relationship between the sides and the angles of the triangle.
Use the fact: [tex]cos x=a[/tex]⇒[tex]x=cos^{-1}(a)+2n\pi,x=2\pi-cos^{-1}(a)+2n\pi[/tex]
[tex]2 cos(3x)=0.9[/tex]
Divide both sides by 2
[tex]cos(3x)=\frac{0.9}{2}=0.45[/tex]
[tex]3x=cos^{-1}(0.45)+2n\pi,3x=2\pi- cos^{-1}(0.45)+2n\pi[/tex]
So,
[tex]x=\frac{cos^{-1}(0.45)+2n\pi}{3} ,x=\frac{2\pi- cos^{-1}(0.45)+2n\pi}{3}[/tex]
