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Chapter 4: Problem 50

Find a formula for converting from grads to radians.

Short Answer

Expert verified
To convert an angle from grads to radians, use the following formula: \( \textit{angle in radians} = \textit{angle in grads} 脳 \frac{\pi}{200} \)

Step by step solution

01

Understanding Grads and Radians

Grads and radians are both units of measuring angles. Radians are commonly used in mathematics, while grads are mainly used in some fields of engineering and navigation. A full circle (or a full turn) has an angle of 2蟺 radians or 400 grads.
02

Finding the Conversion Factor

We know that a full turn is equivalent both in grads and radians. Therefore, we can write an equation relating the two: \( 2\pi~radians = 400~grads \) Now, to find the conversion factor, let's divide both sides of the equation by 400 grads: \( \frac{2\pi~radians}{400~grads} = 1 \) \( \frac{\pi~radians}{200~grads} = 1 \) Now the conversion factor is clear: to convert an angle in grads to radians, we simply need to multiply the angle in grads by \(\frac{\pi}{200}\).
03

Conversion Formula for Grads to Radians

To convert an angle from grads to radians, use the following formula: \( \textit{angle in radians} = \textit{angle in grads} 脳 \frac{\pi}{200} \) This formula allows us to easily convert any angle measured in grads to radians.

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