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

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

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Standard form: find x- and y-interceptsright chevron icon

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 for degrees to radians: To convert degrees to radians, we use the conversion factor that π \pi radians is equivalent to 180180 degrees. The formula to convert degrees to radians is given by:\newlineradians=degrees×π180 \text{radians} = \text{degrees} \times \frac{\pi}{180}
  2. Applying the formula to the given angle: 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. Performing the multiplication to find the radian measure: Perform the multiplication to find the radian measure:\newlineθradians=260180π \theta_{\text{radians}} = \frac{260}{180} \pi \newlineθradians=139π \theta_{\text{radians}} = \frac{13}{9} \pi \newlineThis is the exact radian measure of the angle.

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