To express [tex]\(\theta\)[/tex] as a function of [tex]\(x\)[/tex] using an inverse trigonometric function, let's consider the relationship between [tex]\(\theta\)[/tex] and [tex]\(x\)[/tex] in the context of right triangle trigonometry.
We know that the cosine of an angle [tex]\(\theta\)[/tex] is given by the ratio of the adjacent side to the hypotenuse in a right triangle:
[tex]\[ \cos(\theta) = x \][/tex]
To find the angle [tex]\(\theta\)[/tex], we need to take the inverse cosine (also known as arccosine) of both sides:
[tex]\[ \theta = \arccos(x) \][/tex]
Thus, [tex]\(\theta\)[/tex] can be written as a function of [tex]\(x\)[/tex] using the arccosine function:
[tex]\[ \theta = \arccos(x) \][/tex]
So, the final answer is:
[tex]\[ \theta = \arccos(x) \][/tex]
