What is [tex]75^\circ[/tex] expressed in radians? Choose the most simplified expression.

A. [tex]\frac{5\pi}{12}[/tex]

B. [tex]\frac{5\pi}{3}[/tex]

C. [tex]\frac{\pi}{4}[/tex]

D. [tex]\frac{\pi}{3}[/tex]



Answer :

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].