Convert the following angle from degrees to radians. Express your answer in simplest form.
585, degrees
585
∘
To convert from degrees to radians, we use the conversion factor π/180.
So, we have:
585 degrees * (π/180 radians/degree)
To simplify the expression, we divide the numerator and denominator by the greatest common divisor, which is 15:
585 degrees * (π/180 radians/degree) / 15
= 39π/12 radians
Simplifying the fraction further, we can divide the numerator and denominator by 3:
= 13π/4 radians
Therefore, 585 degrees is equivalent to 13π/4 radians.