Question 3 (4 points) 1. To find the radian equivalent of \( 115^{\circ} \), I would multiply it by pil/180 . The result would be equal to \( \qquad \) 23pi/36 radians. 2. To find the degree equivalent of \( \frac{7 \pi}{5} \) , I would multiply it by \( \qquad \) 180/pi . The result would be equal to 252 。 \( \qquad \) degrees. Blank 1: pi/180 Blank 2: \( 23 \mathrm{pi} / 36 \) Blank 3: \( 180 / \mathrm{pi} \) Blank 4: 252 o

Did you know that the concept of radians dates back to ancient Greece? While the early mathematicians used degrees for angles, radians were later introduced by mathematicians like Roger Cotes and Leonhard Euler in the 17th century. This fascinating shift made calculations involving circles and angles much simpler and paved the way for advancements in calculus and trigonometry! When it comes to real-world applications, understanding radians is crucial, especially in fields like engineering and physics. Engineers often deal with angular motion, and using radians allows for direct interaction with mathematical functions like sine and cosine, making it easier to model various phenomena, from robotics to wave patterns. So, next time you’re calculating trajectories or analyzing wave functions, remember that those radians are your best friends!