To find the value of [tex]\( x \)[/tex] using a trigonometric expression, we can use the tangent function. In this case, we specifically need the tangent of [tex]\( \frac{a}{b} \)[/tex]. Here's the detailed step-by-step solution:
1. Identify the variables and values:
- Let [tex]\( a \)[/tex] and [tex]\( b \)[/tex] be given values.
- From the results, we have [tex]\( a = 1 \)[/tex] and [tex]\( b = 1 \)[/tex].
2. Set up the trigonometric expression:
- We need to find [tex]\( \tan \left(\frac{a}{b}\right) \)[/tex].
3. Determine [tex]\( \frac{a}{b} \)[/tex]:
- Since both [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are equal to [tex]\( 1 \)[/tex], [tex]\( \frac{a}{b} = \frac{1}{1} = 1 \)[/tex].
4. Calculate [tex]\( \tan(1) \)[/tex]:
- Use this result to find the tangent of 1 radian.
- Note that the value for [tex]\( \tan(1) \approx 1.5574077246549023 \)[/tex].
Thus, the trigonometric expression used to find the value of [tex]\( x \)[/tex] is [tex]\( \tan \left(\frac{a}{b}\right) \)[/tex]. Given that [tex]\( \frac{a}{b} \)[/tex] equals [tex]\( 1 \)[/tex], the value of [tex]\( x \)[/tex] is approximately [tex]\( 1.5574077246549023 \)[/tex].
So the final answer is:
[tex]\[ \tan \left(\frac{1}{1}\right) = 1.5574077246549023 \][/tex]
