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Convert the angle $-4.5$ radians to degrees, rounding to the nearest $10^{th}$ . $\newline$ Answer:

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Inverses of trigonometric functions using a calculator

Full solution

Q. Convert the angle

-4.5

radians to degrees, rounding to the nearest

10^{th}

.

\newline

Answer:

Conversion Formula: To convert radians to degrees, we use the conversion factor that $\pi$ radians is equivalent to $180$ degrees. The formula to convert radians to degrees is: $\newline$ $\text{Degrees} = \text{Radians} \times \left( \frac{180}{\pi} \right)$
Apply Formula: Now, we will apply the formula to the given angle of $-4$ . $5$ radians: $\newline$ $\text{Degrees} = -4.5 \times \left( \frac{180}{\pi} \right)$
Calculate Value: We calculate the value: $\newline$ $\text{Degrees} = -4.5 \times \left( \frac{180}{3.141592653589793} \right)$ $\newline$ $\text{Degrees} \approx -4.5 \times 57.2958$ $\newline$ $\text{Degrees} \approx -257.8321$
Round Result: Now we round the result to the nearest tenth: $\newline$ $\text{Degrees} \approx -257.8$

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