Solve for x. Round to the nearest tenth of a degree, if necessary.
The Correct Answer and Explanation is :
I’m unable to access the image directly, but based on the URL, it appears to be a trigonometric equation. Let’s consider a general trigonometric equation and solve for ( x ). For example, if the equation is:
[ \sin(x) = 0.5 ]
Step 1: Identify the general solution
The sine function equals 0.5 at specific angles. From trigonometric tables or a calculator, we know:
[ \sin(30^\circ) = 0.5 ]
Since the sine function is positive in both the first and second quadrants, the general solutions are:
[ x = 30^\circ + 360^\circ n \quad \text{or} \quad x = 150^\circ + 360^\circ n ]
where ( n ) is any integer.
Step 2: Find the solutions within a specific interval
If the problem asks for solutions within a specific interval, such as ( 0^\circ \leq x < 360^\circ ), we substitute ( n = 0 ) into the general solutions:
- For ( x = 30^\circ + 360^\circ n ), when ( n = 0 ), ( x = 30^\circ ).
- For ( x = 150^\circ + 360^\circ n ), when ( n = 0 ), ( x = 150^\circ ).
Thus, the solutions within the interval ( 0^\circ \leq x < 360^\circ ) are:
[ x = 30^\circ \quad \text{and} \quad x = 150^\circ ]
Step 3: Round to the nearest tenth of a degree
Both solutions are already whole numbers, so rounding to the nearest tenth of a degree gives:
[ x = 30.0^\circ \quad \text{and} \quad x = 150.0^\circ ]
Conclusion
The solutions to the equation ( \sin(x) = 0.5 ) within the interval ( 0^\circ \leq x < 360^\circ ) are:
[ x = 30.0^\circ \quad \text{and} \quad x = 150.0^\circ ]
If the equation in the image differs from this example, please provide the specific equation, and I can offer a more tailored solution.