Convert $$ 122^{\circ} 24^{\prime} 36^{\prime \prime} $$ from degrees to radians. Round to 4 decimal places. $$ 122^{\circ} 24^{\prime} 36^{\prime \prime} \approx \square $$ radians

Question

UpStudy AI · Accepted Answer

We start by converting the entire angle into degrees. The given angle is  
$$
122^{\circ} 24^{\prime} 36^{\prime\prime}.
$$

1. Convert minutes and seconds to degrees:
   - There are $$60$$ minutes in a degree, so  
     $$
     24^{\prime} = \frac{24}{60} = 0.4^{\circ}.
     $$
   - There are $$3600$$ seconds in a degree, so  
     $$
     36^{\prime\prime} = \frac{36}{3600} = 0.01^{\circ}.
     $$

2. Sum the degrees:
   $$
   122 + 0.4 + 0.01 = 122.41^{\circ}.
   $$

3. Convert degrees to radians using the conversion factor  
   $$\frac{\pi}{180}$$:
   $$
   122.41^{\circ} \times \frac{\pi}{180} \approx 122.41 \times 0.0174533 \approx 2.1389 \text{ radians}.
   $$

Thus,  
$$
122^{\circ} 24^{\prime} 36^{\prime\prime} \approx 2.1389 \text{ radians}.
$$
$$122^{\circ} 24^{\prime} 36^{\prime\prime} \approx 2.1389$$ radians

Convert from degrees to radians. Round to 4 decimal places.
radians

Upstudy AI Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Trigonometry Questions

Convert from degrees to radians. Round to 4 decimal places. radians