What trigonometric expression can be used to find the value of [tex]$x$[/tex]? Replace [tex]$a$[/tex] and [tex][tex]$b$[/tex][/tex] with the correct values.

[tex] x = \frac{a}{\tan(b)} [/tex]



Answer :

Sure, let's work through this step-by-step!

We are given the trigonometric expression:

[tex]\[ x = \frac{a}{\tan(b)} \][/tex]

We need to find the values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex] and replace them in the expression. According to the data provided:

1. [tex]\( a = 1 \)[/tex]
2. [tex]\( b = 45° \)[/tex] (since the angle is in degrees, it's important to use the degree measure here)

Now, substitute [tex]\( a \)[/tex] and [tex]\( b \)[/tex] into the expression:

[tex]\[ x = \frac{1}{\tan(45°)} \][/tex]

Next, recall that the tangent of 45 degrees is 1:

[tex]\[ \tan(45°) = 1 \][/tex]

So, the expression simplifies to:

[tex]\[ x = \frac{1}{1} \][/tex]

Hence:

[tex]\[ x = 1 \][/tex]

However, given the precision might introduce slight numerical inaccuracies in practical computation, the final value we reported is:

[tex]\[ x \approx 1.0000000000000002\][/tex]

Thus, the trigonometric expression used is:

[tex]\[ x = \frac{1}{\tan(45°)} \][/tex]

And the final value of [tex]\( x \)[/tex] is approximately:

[tex]\[ x \approx 1.0000000000000002\][/tex]