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

Answer:

$a=3.0881$ degrees.

$a=(0.017156)\pi$ rad  or

$a=0.053897$ rad

Step-by-step 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' = $\frac{5}{60}$ degree

For the seconds :

3600'' = 1 degree ⇒

17'' = $\frac{17}{3600}$ degree

Finally :

$a=(3+\frac{5}{60}+\frac{17}{3600})$ 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 = $\frac{(3.0881)2\pi }{360}$ rad

$a=0.053897$ rad

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