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Use an inverse trigonometric function to write [tex]\(\theta\)[/tex] as a function of [tex]\(x\)[/tex].

[tex]\[
\theta = \square
\][/tex]

Sagot :

GinnyAnsweridn
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]
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