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Chapter 5: Problem 119

Determine whether each statement makes sense or does not make sense, and explain your reasoning. When I convert degrees to radians, I multiply by \(1,\) choosing \(\frac{\pi}{180^{\circ}}\) for 1

Short Answer

Expert verified
The statement makes sense when interpreted as 'when converting degrees to radians, I multiply by the 'equivalence' of 1, which is \(\frac{\pi}{180^{\circ}}\)' - the conversion of degrees to radians is done by multiplying with \(\frac{\pi}{180^{\circ}}\) which is equivalent to \(1\) in terms of degrees to radians conversion.

Step by step solution

01

Understand Degrees to Radian Conversion

Before evaluating the statement, it's crucial to understand the conversion process from degrees to radians. The conversion factor is indeed \(\frac{\pi}{180^{\circ}}\), meaning for every degree, there are \(\frac{\pi}{180}\) radians.
02

Evaluate Statement

Looking at the statement 'when I convert degrees to radians, I multiply by 1, choosing \(\frac{\pi}{180^{\circ}}\) for 1', initially it seems confusing because \(1\) is not typically the conversion factor for degrees to radians.
03

Unfold the Meaning

While it's not normally expressed in this way, the statement in the exercise could be a different approach of saying 'when converting degrees to radians, I multiply by the 'equivalence' of 1, which is \(\frac{\pi}{180^{\circ}}\)'. Coming to this interpretation, the statement can be seen as making sense.

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