Answer:
The expression that represents [tex]\theta[/tex] is
[tex]\theta=arccos(\frac{x}{6})[/tex]
Step-by-step explanation:
The trigonometric equation given to us is
[tex]cos(\theta)=\frac{x}{6}[/tex]
We take the cosine inverse of both sides to obtain,
[tex]arccos(cos(\theta))=arccos(\frac{x}{6})[/tex]
Recall that, the composition of a function of x and its inverse produces x.
That is [tex]f(f^{-1}(x))=x[/tex] or
[tex]f^{-1}(f(x))=x[/tex]
Similarly, [tex]arccos(cos(\theta))=\theta[/tex]
This implies that,
[tex]\theta=arccos(\frac{x}{6})[/tex]
The correct answer is C.
