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If theta=(2pi)/(3) radians, what is the value of theta in degrees?

If θ=2π3 \theta=\frac{2 \pi}{3} 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=2π3 \theta=\frac{2 \pi}{3} radians, what is the value of θ \theta in degrees?
  1. Conversion factor: To convert radians to degrees, we use the conversion factor that π\pi radians is equal to 180180 degrees.
  2. Multiply by conversion factor: We multiply the given angle in radians by the conversion factor (180/π)(180/\pi) to find the angle in degrees.\newlineθ\theta in degrees = θ\theta in radians ×(180/π)\times (180/\pi)
  3. Substitute given value: Substitute the given value of θ\theta in radians into the conversion formula.\newlineθ\theta in degrees = (2π3)×(180π)\left(\frac{2\pi}{3}\right) \times \left(\frac{180}{\pi}\right)
  4. Simplify expression: Simplify the expression by canceling out the π\pi in the numerator and the denominator.\newlineθ\theta in degrees =2×60= 2 \times 60
  5. Calculate final value: Calculate the final value. θ\theta in degrees = 120120

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