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Convert the angle theta=(133 pi)/(72) radians to degrees. Express your answer exactly. theta=◻" 。 "

Convert the angle θ=133π72 \theta=\frac{133 \pi}{72} radians to degrees.\newlineExpress your answer exactly.\newlineθ=□∘ \theta=\square^{\circ}

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Full solution

Q. Convert the angle θ=133π72 \theta=\frac{133 \pi}{72} radians to degrees.\newlineExpress your answer exactly.\newlineθ=□∘ \theta=\square^{\circ}
  1. Conversion factor for radians to degrees: 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:\newlineθ\theta (degrees) = θ\theta (radians) ×(180π)\times \left(\frac{180}{\pi}\right)
  2. Applying the conversion formula: Now, we apply the formula to the given angle θ=133π72 \theta = \frac{133 \pi}{72} radians.\newlineθ \theta (degrees) = (133π72)×180π \left(\frac{133 \pi}{72}\right) \times \frac{180}{\pi}
  3. Simplifying the expression: We can simplify the expression by canceling out the π\pi terms and multiplying the remaining terms.θ(degrees)=(133×18072)\theta (\text{degrees}) = \left(\frac{133 \times 180}{72}\right)
  4. Performing the multiplication and division: Now, we perform the multiplication and division to find the exact value in degrees. \newlineθ\theta (degrees) = 2394072\frac{23940}{72}
  5. Simplifying the fraction: We simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, if possible.\newlineHowever, in this case, 2394023940 and 7272 do not have a common divisor other than 11, so the fraction is already in its simplest form.\newlineθ\theta (degrees) = 2394072\frac{23940}{72}
  6. Expressing the answer exactly: To express the answer exactly, we leave the fraction as it is without converting it to a decimal.\newlineθ\theta (degrees) = 2394072\frac{23940}{72}

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