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Convert the angle
theta=230^(@) to radians.
Express your answer exactly.

Convert the angle $\theta=230^{\circ}$ to radians. $\newline$ Express your answer exactly. $\newline$ $\theta=\square \text { radians }$

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Standard form: find x- and y-intercepts

Full solution

Q. Convert the angle

\theta=230^{\circ}

to radians.

\newline

Express your answer exactly.

\newline

\theta=\square \text { radians }

Conversion factor for degrees to radians: To convert degrees to radians, we use the conversion factor that $\pi$ radians is equal to $180$ degrees. The formula to convert degrees to radians is: $\newline$ radians = degrees $\times \left(\frac{\pi}{180}\right)$
Applying the formula to $\theta$ : Now we apply the formula to $\theta = 230$ degrees. $\text{radians} = 230 \times \left(\frac{\pi}{180}\right)$
Simplifying the expression: Simplify the expression by multiplying $230$ by $\pi$ and then dividing by $180$ . $\text{radians} = \frac{230 \times \pi}{180}$
Dividing numerator and denominator by greatest common divisor: We can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is $10$ in this case. $\newline$ radians $= (23 \times \pi) / 18$
Final answer: The fraction $(23 \times \pi) / 18$ is already in its simplest form, so this is our final answer.

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