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Convert the angle theta=(8pi)/(9) radians to degrees.

Convert the angle θ=8π9 \theta=\frac{8 \pi}{9} radians to degrees.

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Full solution

Q. Convert the angle θ=8π9 \theta=\frac{8 \pi}{9} radians to degrees.
  1. Convert to degrees: To convert radians to degrees, we use the conversion factor that π\pi radians is equal to 180180 degrees. The formula to convert an angle in radians to degrees is: degrees=radians×(180/π)\text{degrees} = \text{radians} \times (180/\pi).
  2. Apply formula: Now, we apply the formula to θ=8π9\theta=\frac{8\pi}{9} radians. So, we have degrees=8π9×180π\text{degrees} = \frac{8\pi}{9} \times \frac{180}{\pi}.
  3. Simplify expression: We can simplify the expression by canceling out the pi terms. This leaves us with degrees=89×180\text{degrees} = \frac{8}{9} \times 180.
  4. Perform multiplication: Next, we perform the multiplication: degrees=89×180=160\text{degrees} = \frac{8}{9} \times 180 = 160.

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