To convert an angle from radians to degrees, we need to know the relationship between radians and degrees. This relationship is given by the fact that [tex]\( \pi \)[/tex] radians is equivalent to [tex]\( 180^\circ \)[/tex].
Let's convert the given angle [tex]\( \frac{3 \pi}{4} \)[/tex] radians to degrees step by step.
1. We know that [tex]\( \pi \)[/tex] radians is equal to [tex]\( 180^\circ \)[/tex].
2. To find the angle in degrees, we can set up a proportion:
[tex]\[
\frac{3 \pi}{4} \text{ radians} \times \frac{180^\circ}{\pi \text{ radians}}
\][/tex]
3. Notice that the [tex]\( \pi \)[/tex] in the numerator and denominator cancels out:
[tex]\[
\frac{3 \times 180^\circ}{4}
\][/tex]
4. Multiply the numbers in the fraction:
[tex]\[
\frac{540^\circ}{4} = 135^\circ
\][/tex]
Therefore, the angle [tex]\( \frac{3 \pi}{4} \)[/tex] radians is exactly [tex]\( 135^\circ \)[/tex]. Hence, the correct answer is:
(d) [tex]\( 135^\circ \)[/tex]
