To solve the problem, we need to examine the trigonometric expression given:
[tex]\[ x = \operatorname{acos}(b) \][/tex]
Here, [tex]\( \operatorname{acos} \)[/tex] represents the arccosine function. The arccosine function is used to find the angle whose cosine is the given number [tex]\( b \)[/tex].
From the layout of the equation, it seems we have to replace some values with specific numbers to find [tex]\( x \)[/tex]. However, this problem lacks additional context or a diagram to correctly identify values for [tex]\( a \)[/tex] and [tex]\( b \)[/tex].
The trigonometric relationship for the arccosine function is:
[tex]\[ \cos(x) = b \][/tex]
If there is additional context or information, such as a right triangle, we would use [tex]\(\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}\)[/tex] and then solve for [tex]\( \theta \)[/tex] using the arccosine function.
For example, if the problem had a triangle setup:
- If the adjacent side of the angle [tex]\( x \)[/tex] is [tex]\( a \)[/tex]
- And the hypotenuse is [tex]\( c \)[/tex],
Then [tex]\[ b = \frac{a}{c} \][/tex]
Therefore, the exact values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex] should come from the given specific setup or triangle. If this setup were known, plugging in the relevant values into the expression [tex]\( x = \operatorname{acos}(b) \)[/tex] would be straightforward.
Since we do not have that specific setup in this case, we cannot provide numerical substitutions for [tex]\( a \)[/tex] and [tex]\( b \)[/tex]. However, the form of the correct answer remains as:
[tex]\[ x = \operatorname{acos}(b) \][/tex]
This indicates that [tex]\( b \)[/tex] is the cosine of the angle [tex]\( x \)[/tex].
If more context or details were provided, such as a triangle diagram or specific lengths, we could determine the exact values for [tex]\( a \)[/tex] and [tex]\( b \)[/tex].
