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If theta=(pi)/(12) radians, what is the value of theta in degrees?

If θ=π12 \theta=\frac{\pi}{12} 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=π12 \theta=\frac{\pi}{12} radians, what is the value of θ \theta in degrees?
  1. Use Conversion Factor: To convert radians to degrees, we use the conversion factor that 180180 degrees is equal to π\pi radians. The formula to convert from radians to degrees is: degrees=radians×(180π)\text{degrees} = \text{radians} \times (\frac{180}{\pi}).
  2. Substitute Theta: Substitute θ=(π/12)\theta = (\pi/12) radians into the conversion formula: degrees=(π/12)×(180/π)\text{degrees} = (\pi/12) \times (180/\pi).
  3. Simplify Expression: Simplify the expression by canceling out π\pi in the numerator and the denominator: degrees=(112)×180\text{degrees} = \left(\frac{1}{12}\right) \times 180.
  4. Calculate Value: Calculate the value: degrees=18012=15\text{degrees} = \frac{180}{12} = 15.

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