It seems you are trying to solve an equation involving a sine function. However, the equation you provided has a couple of issues because it isn't clear what "sin" is referring to in terms of angle or radian.
If we assume you meant \(11 \times 22 \times \sin(\theta) = 121\), we can simplify this.
First, calculate \(11 \times 22\):
\[ 11 \times 22 = 242 \]
Now substituting back into the equation gives:
\[ 242 \times \sin(\theta) = 121 \]
Now, divide both sides by \(242\):
\[ \sin(\theta) = \frac{121}{242} \]
This simplifies to:
\[ \sin(\theta) = \frac{1}{2} \]
Now, we can find the value of \(\theta\). The sine of an angle equals \(\frac{1}{2}\) at:
\[ \theta = 30^\circ \quad \text{and} \quad \theta = 150^\circ \]
For radians, these angles are:
\[ \theta = \frac{\pi}{6} \quad \text{and} \quad \theta = \frac{5\pi}{6} \]
Remember that sine is periodic, so there are infinitely many solutions depending on the period of the sine function:
\[ \theta = 30^\circ + k \cdot 360^\circ \quad \text{and} \quad \theta = 150^\circ + k \cdot 360^\circ \quad \text{for any integer } k \]
Or in radians:
\[ \theta = \frac{\pi}{6} + 2k\pi \quad \text{and} \quad \theta = \frac{5\pi}{6} + 2k\pi \quad \text{for any integer } k \]
If you meant something different, please clarify!