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

Understanding radians and degrees: Understand the relationship between radians and degrees. One complete revolution around a circle is 360 degrees, which is also equal to 2π radians. Therefore, the conversion factor between radians and degrees is 180 degrees per π radians.Converting radians to degrees: Convert (3π)/2 radians to degrees. To convert radians to degrees, multiply the radian measure by the conversion factor (180/π). So, θ in degrees is (3π)/2 * (180/π).Performing the calculation: Perform the calculation. (3π)/2 * (180/π) = (3/2) * 180 = 3 * 90 = 270Verifying the result: Verify the result. Since (3π)/2 radians is three-quarters of the way around a circle, and a full circle is 360 degrees, three-quarters of 360 degrees is indeed 270 degrees. This confirms that our calculation is correct.

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

If $\theta=\frac{3 \pi}{2}$ radians, what is the value of $\theta$ in degrees?

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Q. If

\theta=\frac{3 \pi}{2}

radians, what is the value of

\theta

in degrees?

Understanding radians and degrees: Understand the relationship between radians and degrees. $\newline$ One complete revolution around a circle is $360^\circ$ , which is also equal to $2\pi$ radians. Therefore, the conversion factor between radians and degrees is $180^\circ$ per $\pi$ radians.
Converting radians to degrees: Convert $(3\pi)/2$ radians to degrees. $\newline$ To convert radians to degrees, multiply the radian measure by the conversion factor $(180/\pi)$ . $\newline$ So, $\theta$ in degrees is $(3\pi)/2 \times (180/\pi)$ .
Performing the calculation: Perform the calculation. $\newline$ $(\frac{3\pi}{2}) \times (\frac{180}{\pi}) = (\frac{3}{2}) \times 180$ $\newline$ $= 3 \times 90$ $\newline$ $= 270$
Verifying the result: Verify the result. $\newline$ Since $(\frac{3\pi}{2})$ radians is three-quarters of the way around a circle, and a full circle is $360$ degrees, three-quarters of $360$ degrees is indeed $270$ degrees. This confirms that our calculation is correct.