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

Conversion factor for radians to degrees: To convert radians to degrees, we use the conversion factor that π radians is equal to 180 degrees. The formula to convert from radians to degrees is: θ (degrees) = θ (radians) × (180/π)Applying the conversion formula: Now, we apply the formula to the given angle θ = (133 π) / (72) radians. θ (degrees) = ((133 π) / (72)) × (180/π)Simplifying the expression: We can simplify the expression by canceling out the π terms and multiplying the remaining terms. θ (degrees) = (133 × 180) / 72Performing the multiplication and division: Now, we perform the multiplication and division to find the exact value in degrees. θ (degrees) = 23940 / 72Simplifying the fraction: We simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, if possible. However, in this case, 23940 and 72 do not have a common divisor other than 1, so the fraction is already in its simplest form. θ (degrees) = 23940 / 72Expressing the answer exactly: To express the answer exactly, we leave the fraction as it is without converting it to a decimal. θ (degrees) = 23940 / 72

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Full solution

Q. Convert the angle

\theta=\frac{133 \pi}{72}

radians to degrees.

\newline

Express your answer exactly.

\newline

\theta=\square^{\circ}

Conversion factor for radians to degrees: To convert radians to degrees, we use the conversion factor that $\pi$ radians is equal to $180$ degrees. The formula to convert from radians to degrees is: $\newline$ $\theta$ (degrees) = $\theta$ (radians) $\times \left(\frac{180}{\pi}\right)$
Applying the conversion formula: Now, we apply the formula to the given angle $\theta = \frac{133 \pi}{72}$ radians. $\newline$ $\theta$ (degrees) = $\left(\frac{133 \pi}{72}\right) \times \frac{180}{\pi}$
Simplifying the expression: We can simplify the expression by canceling out the $\pi$ terms and multiplying the remaining terms. $\theta (\text{degrees}) = \left(\frac{133 \times 180}{72}\right)$
Performing the multiplication and division: Now, we perform the multiplication and division to find the exact value in degrees. $\newline$ $\theta$ (degrees) = $\frac{23940}{72}$
Simplifying the fraction: We simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, if possible. $\newline$ However, in this case, $23940$ and $72$ do not have a common divisor other than $1$ , so the fraction is already in its simplest form. $\newline$ $\theta$ (degrees) = $\frac{23940}{72}$
Expressing the answer exactly: To express the answer exactly, we leave the fraction as it is without converting it to a decimal. $\newline$ $\theta$ (degrees) = $\frac{23940}{72}$