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To convert an angle measured in radians to degrees, you can use the conversion factor that [tex]\(180^\circ\)[/tex] is equivalent to [tex]\(\pi\)[/tex] radians. Here's a step-by-step process to convert [tex]\(\frac{5\pi}{3}\)[/tex] radians into degrees:
1. Write down the given radians:
[tex]\[ \frac{5\pi}{3} \text{ radians} \][/tex]
2. Use the conversion factor:
[tex]\[ 1 \text{ radian} = \frac{180^\circ}{\pi} \][/tex]
3. Multiply the given radian measure by the conversion factor:
[tex]\[ \frac{5\pi}{3} \times \frac{180^\circ}{\pi} \][/tex]
4. Cancel out the [tex]\(\pi\)[/tex] in the numerator and denominator:
[tex]\[ \frac{5 \times 180^\circ}{3} \][/tex]
5. Simplify the multiplication and division:
[tex]\[ \frac{900^\circ}{3} = 300^\circ \][/tex]
Therefore, [tex]\(\frac{5\pi}{3}\)[/tex] radians is equal to [tex]\(300^\circ\)[/tex].
1. Write down the given radians:
[tex]\[ \frac{5\pi}{3} \text{ radians} \][/tex]
2. Use the conversion factor:
[tex]\[ 1 \text{ radian} = \frac{180^\circ}{\pi} \][/tex]
3. Multiply the given radian measure by the conversion factor:
[tex]\[ \frac{5\pi}{3} \times \frac{180^\circ}{\pi} \][/tex]
4. Cancel out the [tex]\(\pi\)[/tex] in the numerator and denominator:
[tex]\[ \frac{5 \times 180^\circ}{3} \][/tex]
5. Simplify the multiplication and division:
[tex]\[ \frac{900^\circ}{3} = 300^\circ \][/tex]
Therefore, [tex]\(\frac{5\pi}{3}\)[/tex] radians is equal to [tex]\(300^\circ\)[/tex].
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