To convert an angle from degrees to radians, you can use the formula:
[tex]\[ \text{radians} = \text{degrees} \times \left(\frac{\pi}{180}\right) \][/tex]
Given that the angle is [tex]\(75^\circ\)[/tex], we can substitute this value into the formula:
[tex]\[ \text{radians} = 75 \times \left(\frac{\pi}{180}\right) \][/tex]
Now, simplify the fraction:
[tex]\[ \frac{75}{180} = \frac{75 \div 15}{180 \div 15} = \frac{5}{12} \][/tex]
Therefore, we have:
[tex]\[ \text{radians} = \frac{5}{12} \pi \][/tex]
So, [tex]\(75^\circ\)[/tex] expressed in radians is:
[tex]\[ \frac{5}{12} \pi \][/tex]
In decimal form, this is approximately:
[tex]\[ 1.3089969389957472 \][/tex]
Hence, the exact value in its most simplified form is [tex]\(\frac{5}{12} \pi\)[/tex], and the approximate decimal value is [tex]\(1.3089969389957472\)[/tex].
