# Question 6d7fc

Oct 29, 2017

As there are $2 \pi$ radians in a circle, one rad = $\frac{360}{2 \pi}$ degrees and one degree is $\frac{2 \pi}{360}$ radians.

#### Explanation:

From here it is not too tricky ...

69^@ 49’ 6” = 69.818^@#

So that is $69.818 \times \frac{2 \pi}{360} ^ \circ$ rad

Oct 29, 2017

#### Explanation:

Convert the minutes and second values to the equivalent decimal fractions of a degree.

one arc second is $\frac{1}{3600}$ of a degree, and you've got six of them, so that comes to: .0016666... (repeating) degrees.

An arc minute is $\frac{1}{60}$ of a degree, and you've got 49 of them, which works out to: .8166666...(repeating) degrees.

69 + .81666 + .0016666 = 69.8183333....(repeating) degrees.

$\frac{69.818333 \ldots}{360} = \frac{r a \mathrm{di} a n s}{2 \pi}$