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If theta=(pi)/(9) radians, what is the value of theta in degrees?

If θ=π9 \theta=\frac{\pi}{9} radians, what is the value of θ \theta in degrees?

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Inverses of csc, sec, and cotright chevron icon

Full solution

Q. If θ=π9 \theta=\frac{\pi}{9} radians, what is the value of θ \theta in degrees?
  1. Conversion Formula: To convert radians to degrees, we use the conversion factor that 180180 degrees is equal to pi radians. The formula to convert from radians to degrees is:\newlinedegrees=radians×(180π) \text{degrees} = \text{radians} \times \left( \frac{180}{\pi} \right)
  2. Substitution of Theta: Now we substitute theta which is π9\frac{\pi}{9} radians into the formula:\newlinedegrees=(π9)×(180π) \text{degrees} = \left( \frac{\pi}{9} \right) \times \left( \frac{180}{\pi} \right)
  3. Simplification: We can simplify the expression by canceling out the pi terms:\newlinedegrees=1809 \text{degrees} = \frac{180}{9}
  4. Final Calculation: Divide 180180 by 99 to find the value in degrees:\newlinedegrees=20 \text{degrees} = 20

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