Problem 119 - Algebra and Trigonometry

Question

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

Step-by-Step Solution

Answer

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 1: 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.

Step 2: 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.

Step 3: 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.