Solve for x :
`sin(x+10^(@))=1/2`

Answer

To solve the equation \( \sin(x + 10^\circ) = \frac{1}{2} \), we can follow these steps:

### Step 1: Identify the angle whose sine is \( \frac{1}{2} \)
We know that:
\[ \sin(30^\circ) = \frac{1}{2} \]
Thus, we can set up the equation:
\[ x + 10^\circ = 30^\circ \]

### Step 2: Solve for \( x \)
Now, we will isolate \( x \) by subtracting \( 10^\circ \) from both sides:
\[ x = 30^\circ - 10^\circ \]
\[ x = 20^\circ \]

### Step 3: Consider the general solution
The sine function is periodic, and it has a periodicity of \( 360^\circ \). Therefore, we also need to consider the second angle where sine is \( \frac{1}{2} \):
\[ x + 10^\circ = 180^\circ - 30^\circ \]
This gives us:
\[ x + 10^\circ = 150^\circ \]
Now, solving for \( x \):
\[ x = 150^\circ - 10^\circ \]
\[ x = 140^\circ \]

### Final Solutions
Thus, the solutions for \( x \) are:
\[ x = 20^\circ \quad \text{and} \quad x = 140^\circ \]