Find `- 47^(@) 30'` in radian measure.

Options

A. `(19)/(72)pi`
B. `(-19)/(72) pi`
C. `(26pi)/(9)`
D. `(5pi)/(36)`

Answer

To convert the angle \(-47^\circ 30'\) into radians, we can follow these steps:

### Step 1: Convert minutes to degrees
We know that \(1 \text{ degree} = 60 \text{ minutes}\). Therefore, \(30 \text{ minutes}\) can be converted to degrees as follows:

\[ 30' = \frac{30}{60} = 0.5^\circ \]

### Step 2: Combine degrees and minutes
Now, we can express \(-47^\circ 30'\) in degrees:

\[ -47^\circ 30' = -47^\circ - 0.5^\circ = -47.5^\circ \]

### Step 3: Convert degrees to radians
To convert degrees to radians, we use the conversion factor \( \frac{\pi \text{ radians}}{180^\circ} \). Therefore, we can convert \(-47.5^\circ\) to radians:

\[ -47.5^\circ = -47.5 \times \frac{\pi}{180} \]

### Step 4: Simplify the expression
Now we can simplify the expression:

\[ -47.5 \times \frac{\pi}{180} = -\frac{47.5\pi}{180} \]

### Step 5: Convert 47.5 to a fraction
We can express \(47.5\) as a fraction:

\[ 47.5 = \frac{95}{2} \]

Thus, we can rewrite the expression:

\[ -\frac{47.5\pi}{180} = -\frac{\frac{95}{2}\pi}{180} = -\frac{95\pi}{360} \]

### Step 6: Simplify the fraction
Now we simplify \(-\frac{95\pi}{360}\):

We can divide both the numerator and the denominator by 5:

\[ -\frac{95\pi}{360} = -\frac{19\pi}{72} \]

### Final Answer
Thus, the angle \(-47^\circ 30'\) in radian measure is:

\[ -\frac{19\pi}{72} \text{ radians} \]