Determine the reference angle for $ frac{5pi}{3} $ radians and express it in degrees and radians

To find the reference angle for $ \frac{5\pi}{3} $ radians, we need to determine its corresponding acute angle in the first quadrant.

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First, convert $ \frac{5\pi}{3} $ to degrees:

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$ \frac{5\pi}{3} \times \frac{180^\circ}{\pi} = 300^\circ $

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Since 300° is in the fourth quadrant, the reference angle is:

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$ 360^\circ – 300^\circ = 60^\circ $

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Convert 60° back to radians:

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$ 60^\circ \times \frac{\pi}{180^\circ} = \frac{\pi}{3} $

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Therefore, the reference angle for $ \frac{5\pi}{3} $ radians is $ 60^\circ $ or $ \frac{\pi}{3} $ radians.

To find the reference angle of $ frac{5pi}{3} $ radians, first convert it to degrees:

$ frac{5pi}{3} imes frac{180^circ}{pi} = 300^circ $

The angle is in the fourth quadrant, so its reference angle is:

$ 360^circ – 300^circ = 60^circ $

Convert 60° to radians:

$ 60^circ imes frac{pi}{180^circ} = frac{pi}{3} $

Therefore, the reference angle for $ frac{5pi}{3} $ radians is $ 60^circ $ or $ frac{pi}{3} $ radians.

To find the reference angle for $ frac{5pi}{3} $ radians, convert to degrees:

$ frac{5pi}{3} imes frac{180^circ}{pi} = 300^circ $

Since 300° is in the fourth quadrant:

$ 360^circ – 300^circ = 60^circ $

Convert 60° to radians:

$ 60^circ imes frac{pi}{180^circ} = frac{pi}{3} $

The reference angle is $ 60^circ $ or $ frac{pi}{3} $ radians.

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