If `theta` is an acute angle and `sin(theta+18^(@))=(1)/(2)` , then the value of `theta` in circular measure is :

Options

A. `(pi)/(12)` radians
B. `(pi)/(15)` radians
C. `(2pi)/(5)` radians
D. `(3pi)/(13)` radians

Answer

To solve the problem step by step, we will follow the reasoning from the video transcript.

### Step 1: Set up the equation
We start with the equation given in the problem:
\[ \sin(\theta + 18^\circ) = \frac{1}{2} \]

### Step 2: Identify the angle
We know that \(\sin(30^\circ) = \frac{1}{2}\). Therefore, we can equate:
\[ \theta + 18^\circ = 30^\circ \]

### Step 3: Solve for \(\theta\)
Now, we can isolate \(\theta\) by subtracting \(18^\circ\) from both sides:
\[ \theta = 30^\circ - 18^\circ \]
\[ \theta = 12^\circ \]

### Step 4: Convert degrees to radians
To convert degrees to radians, we use the conversion factor \(\frac{\pi}{180^\circ}\):
\[ \theta = 12^\circ \times \frac{\pi}{180^\circ} \]

### Step 5: Simplify the conversion
Now, we simplify the fraction:
\[ \theta = \frac{12\pi}{180} = \frac{\pi}{15} \]

### Final Answer
Thus, the value of \(\theta\) in circular measure is:
\[ \theta = \frac{\pi}{15} \text{ radians} \]

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