Answer :
Answer:
FALSE because the solutions of 3 cos x + 4 = 6 at the interval (0, 2π] is x = 0.841 and x = 5.442.
Explanation:
Let's solve for the value of x. Here are the steps.
a. Subtract 4 on both sides of the equation.
[tex]3cosx+4-4=6-4[/tex][tex]3cosx=2[/tex]b. Divide both sides of the equation by 3.
[tex]\frac{3cosx}{3}=\frac{2}{3}[/tex][tex]cosx=\frac{2}{3}[/tex]c. Take the inverse of the cosine function.
[tex]x=cos^{-1}\frac{2}{3}[/tex][tex]x=0.841[/tex]One of the solutions is 0.841.
To get the other solution, subtract 0.841 from 2π.
[tex]2\pi-0.841=5.442[/tex]The other solution within the interval (0, 2π) is 5.442 and not 3.983.
Hence, the statement is false.