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.

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LucianoBordoli LucianoBordoli · Answer 1 · 2019-11-21T05:42:05+01:00

Answer:

[tex]a=3.0881[/tex] degrees.

[tex]a=(0.017156)\pi[/tex] rad or

[tex]a=0.053897[/tex] 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' = [tex]\frac{5}{60}[/tex] degree

For the seconds :

3600'' = 1 degree ⇒

17'' = [tex]\frac{17}{3600}[/tex] degree

Finally :

[tex]a=(3+\frac{5}{60}+\frac{17}{3600})[/tex] degrees

[tex]a=3.0881[/tex] degrees.

For radians, the equivalence is :

360 degrees = 2π rad

For a = 3.0881 degrees ⇒

360 degrees = 2π rad

3.0881 degrees = [tex]\frac{(3.0881)2\pi }{360}[/tex] rad

[tex]a=0.053897[/tex] rad

or in terms of π ⇒ [tex]a=(0.017156)\pi[/tex] rad