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Convert the angle theta=260^(@) to radians. Express your answer exactly. theta=◻" radians "

Convert the angle θ=260∘ \theta=260^{\circ} to radians.\newlineExpress your answer exactly.\newlineθ=□ radians  \theta=\square \text { radians }

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Full solution

Q. Convert the angle θ=260∘ \theta=260^{\circ} to radians.\newlineExpress your answer exactly.\newlineθ=□ radians  \theta=\square \text { radians }
  1. Conversion Factor Application: To convert degrees to radians, we use the conversion factor that pi radians is equivalent to 180180 degrees. The formula to convert degrees to radians is:\newlineradians=degrees×π180 \text{radians} = \text{degrees} \times \frac{\pi}{180}
  2. Formula Application: Now, we apply the formula to the given angle θ=260∘ \theta = 260^\circ :\newlineθradians=260∘×π180 \theta_{\text{radians}} = 260^\circ \times \frac{\pi}{180}
  3. Expression Simplification: Simplify the expression by multiplying 260260 by π180 \frac{\pi}{180} :\newlineθradians=260π180 \theta_{\text{radians}} = \frac{260\pi}{180}
  4. Fraction Simplification: To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 2020:\newlineθradians=260π180=13π9 \theta_{\text{radians}} = \frac{260\pi}{180} = \frac{13\pi}{9}

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