# How do you convert 15 degrees 30' into radians?

May 14, 2015

First, let's just state some considerations on degrees and radians.

Degrees are given by integer numbers and decimal numbers, and when they are decimal, the decimal part is base-60 (just like minutes and seconds, for example), which means that 15º30' is the same as saying "15 degrees and a half degree".

Radians are given in function of $\pi$. Let's just remember that 2pi = 360º.

Ok, now, let's just formulate our problem.

2pi = 360º
x = 15º30'

Cross-multiplying these terms (in order to find the radians equivalent to 15º30'):

2pi*15º30' = x*360º
x=2pi*((15º30')/360º)

Let's just deal with degrees as normal numbers.

$x = 2 \pi \cdot \left(\frac{15.5}{360}\right)$
$x = 2 \pi \cdot \left(0.043\right)$

So, your answer is $x = 0.086 \pi$

:)