To convert an angle from degrees to radians, we use the relationship:
[tex]\[ 1 \text{ degree} = \frac{\pi}{180} \text{ radians} \][/tex]
Given the angle is [tex]\( -135^\circ \)[/tex], we can express this conversion with the formula:
[tex]\[ \text{radians} = \text{degrees} \times \frac{\pi}{180} \][/tex]
Substituting [tex]\(-135^\circ\)[/tex] into the formula:
[tex]\[ \text{radians} = -135 \times \frac{\pi}{180} \][/tex]
To simplify this:
[tex]\[ \text{radians} = -135 \times \frac{\pi}{180} = -135 \times \frac{\pi}{180} \][/tex]
[tex]\[ = - \frac{135}{180} \pi \][/tex]
We can simplify the fraction [tex]\(\frac{135}{180}\)[/tex]:
[tex]\[ \frac{135}{180} = \frac{135 \div 45}{180 \div 45} = \frac{3}{4} \][/tex]
So:
[tex]\[ \text{radians} = -\frac{3}{4} \pi \][/tex]
Hence, the radian measure corresponding to [tex]\( -135^\circ \)[/tex] is:
[tex]\[ -\frac{3}{4} \pi \][/tex]
Therefore, the correct answer is:
[tex]\[ -\frac{3}{4} \pi \][/tex]
