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

If θ=3π2 \theta=\frac{3 \pi}{2} 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=3π2 \theta=\frac{3 \pi}{2} radians, what is the value of θ \theta in degrees?
  1. Understanding radians and degrees: Understand the relationship between radians and degrees.\newlineOne complete revolution around a circle is 360∘360^\circ, which is also equal to 2π2\pi radians. Therefore, the conversion factor between radians and degrees is 180∘180^\circ per π\pi radians.
  2. Converting radians to degrees: Convert (3π)/2(3\pi)/2 radians to degrees.\newlineTo convert radians to degrees, multiply the radian measure by the conversion factor (180/π)(180/\pi).\newlineSo, θ\theta in degrees is (3π)/2×(180/π)(3\pi)/2 \times (180/\pi).
  3. Performing the calculation: Perform the calculation.\newline(3π2)×(180π)=(32)×180(\frac{3\pi}{2}) \times (\frac{180}{\pi}) = (\frac{3}{2}) \times 180\newline=3×90= 3 \times 90\newline=270= 270
  4. Verifying the result: Verify the result.\newlineSince (3π2)(\frac{3\pi}{2}) radians is three-quarters of the way around a circle, and a full circle is 360360 degrees, three-quarters of 360360 degrees is indeed 270270 degrees. This confirms that our calculation is correct.

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