To solve the equation [tex]\(\tan(x) = 2\)[/tex], we need to find the angle [tex]\(x\)[/tex] for which the tangent value is 2.
1. Identify the function involved:
- The equation given is [tex]\(\tan(x) = 2\)[/tex].
2. Find the inverse tangent:
- To solve for [tex]\(x\)[/tex], take the inverse tangent (also known as arctangent) of both sides of the equation. That is, [tex]\(x = \arctan(2)\)[/tex].
3. Convert to degrees:
- The value obtained from [tex]\(\arctan(2)\)[/tex] will be an angle in radians. To work in degrees, convert the result from radians to degrees.
4. Calculate the result and round appropriately:
- The value of [tex]\(\arctan(2)\)[/tex] in radians is approximately 1.1071 radians.
- Converting this radians value to degrees yields approximately 63.4349 degrees.
- Rounding the result to the nearest tenth, we get 63.4 degrees.
Given the choices provided:
A. [tex]\(-2.2^{\circ}\)[/tex]
B. [tex]\(1.1^{\circ}\)[/tex]
C. [tex]\(26.6^{\circ}\)[/tex]
D. [tex]\(63.4^{\circ}\)[/tex]
The correct rounded answer to the nearest tenth is [tex]\(63.4^{\circ}\)[/tex].
Therefore, the best answer is D. [tex]\(63.4^{\circ}\)[/tex].
