Question

Occasionally you may encounter an angle that's given in the old fashioned degrees/minutes/second form, as described in the box on page 286 of the textbook. A degree is divided into 60 minutes (or minutes of degree), and a minute (of degree) is divided into 60 seconds. Let a = 3 degree 5'17". Then a = degrees (in decimal notation) and a = radians. Again, enter your answers showing at least 4 digits.

Answer 1

`a=3.0881` degrees.

`a=(0.017156)\pi` rad or

`a=0.053897` rad

Explanation:

Let's start writing some equivalences.

1 degree = 60 minutes = 60'

1 minute = 1' = 60 seconds = 60''

Therefore,

1' = 60'' ⇒ 60' = 3600'' ⇒ 1 degree = 3600''

For a = 3 degree 5'17'' we are going to transform the minutes and the seconds into degrees.

60' = 1 degree ⇒

5' =
`(5)/(60)` degree

For the seconds :

3600'' = 1 degree ⇒

17'' =
`(17)/(3600)` degree

Finally :

`a=(3+(5)/(60)+(17)/(3600))` degrees

`a=3.0881` degrees.

For radians, the equivalence is :

360 degrees = 2π rad

For a = 3.0881 degrees ⇒

360 degrees = 2π rad

3.0881 degrees =
`((3.0881)2\pi )/(360)` rad

`a=0.053897` rad

or in terms of π ⇒
`a=(0.017156)\pi` rad