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Convert the angle theta=(3pi)/(5) radians to degrees. Express your answer exactly. theta=◻" 。 "

Convert the angle θ=3π5 \theta=\frac{3 \pi}{5} radians to degrees.\newlineExpress your answer exactly.\newlineθ=□∘ \theta=\square^{\circ}

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Full solution

Q. Convert the angle θ=3π5 \theta=\frac{3 \pi}{5} radians to degrees.\newlineExpress your answer exactly.\newlineθ=□∘ \theta=\square^{\circ}
  1. Conversion Factor: To convert radians to degrees, we use the conversion factor that π\pi radians is equal to 180180 degrees. The formula to convert from radians to degrees is:\newlinetheta (in degrees) = theta (in radians) ×(180π)\times \left(\frac{180}{\pi}\right)
  2. Apply Formula: Now, we apply the formula to the given angle θ=3π5\theta=\frac{3\pi}{5} radians.θ\theta (in degrees) = 3π5×180π\frac{3\pi}{5} \times \frac{180}{\pi}
  3. Simplify Expression: We can simplify the expression by canceling out the π\pi in the numerator and the denominator.θ\theta (in degrees) = 35×180\frac{3}{5} \times 180
  4. Multiply and Divide: Now, we multiply 33 by 180180 and then divide by 55 to get the degree measure.\newlineθ\theta (in degrees) = (3×180)/5(3 \times 180) / 5\newlineθ\theta (in degrees) = 540/5540 / 5
  5. Find Degree Measure: Finally, we perform the division to find the exact degree measure. θ\theta (in degrees) = 108108

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