Pregunta
By means of the definition of a radian, change the given angles in radians to an equal angle expressed in degrees. -3.411 rad -3.411 rad \( =\square^{\circ} \) (Round to two decimal places as needed.)
Ask by Todd Bryant. in the United States
Nov 08,2024
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
-3.411 rad \( = -195.00^{\circ} \)
Solución
To convert radians to degrees, you can use the conversion factor:
\[
1 \text{ radian} = \frac{180}{\pi} \text{ degrees}
\]
To convert \(-3.411\) radians to degrees, you can multiply by this conversion factor:
\[
-3.411 \text{ rad} \times \frac{180}{\pi} \text{ degrees/radian}
\]
Calculating this:
\[
-3.411 \times \frac{180}{\pi} \approx -3.411 \times 57.2958 \approx -195.0
\]
So, rounding to two decimal places:
\[
-3.411 \text{ rad} \approx -195.00^{\circ}
\]
Thus, the final answer is:
\[
-3.411 \text{ rad} = -195.00^{\circ}
\]
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Extra Insights
To convert radians to degrees, we use the conversion factor \( \frac{180}{\pi} \). So, for -3.411 rad: \[ -3.411 \times \frac{180}{\pi} \approx -3.411 \times 57.2958 \approx -195.37^\circ \] Thus, -3.411 rad \( = -195.37^\circ \) (rounded to two decimal places).

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