Math  /  Trigonometry

QuestionConvert the angle 3π5\frac{3 \pi}{5} from radians to degrees.

Studdy Solution

STEP 1

1. The conversion factor between radians and degrees is 180=π 180^\circ = \pi radians.
2. We need to convert the angle 3π5 \frac{3 \pi}{5} radians to degrees.

STEP 2

1. Understand the conversion factor.
2. Apply the conversion to the given angle.

STEP 3

Recall the conversion factor between radians and degrees. We know that:
180=π radians 180^\circ = \pi \text{ radians}
This means that to convert from radians to degrees, we multiply by 180π \frac{180^\circ}{\pi} .

STEP 4

Apply the conversion factor to the given angle 3π5 \frac{3 \pi}{5} radians. We have:
3π5×180π \frac{3 \pi}{5} \times \frac{180^\circ}{\pi}

STEP 5

Simplify the expression by canceling out π \pi in the numerator and the denominator:
3×1805 \frac{3 \times 180^\circ}{5}

STEP 6

Perform the multiplication and division:
3×1805=5405=108 \frac{3 \times 180}{5} = \frac{540}{5} = 108^\circ
The angle 3π5 \frac{3 \pi}{5} radians is equivalent to:
108 \boxed{108^\circ}

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