Question

Write the radian measure of 5° 37’30”.

Answer 1

We have been given the value of angles in degrees and we know, to change an angle x° to x rad is,

\(x\, rad = x° \times \frac \pi {180°}\)

Also, we have,

\(1^° = 60' \)

\(1' = 60''\)

To convert 30 seconds into degrees, we divide the value by 3600 seconds.

We get,

\(x° = 5°37' \frac{30}{3600}\)

Also, to convert 37 minutes to degrees, we divide 37 min by 60.

\(x° = 5° + (\frac{37}{60°})° + (\frac{36}{3600})°\)

\(x° = 5° + (0.61667)° + (0.00834)°\)

\(x° = 5.625°\)

Now,

The value of this angle in radians will be

\(x \, rad = 5.625 \times \frac \pi {180°}\)

\(x \, rad = 5.625 \times \frac 1 {180°} \times \frac{22}7\)

\(x \, rad = 0.03125 \times \frac{22}7\)

\(x \, rad = 0.098125°\)

Hence, the value of the given angles in degrees to radians is 0.098125 radians.

Answer 2

We know that, 60” = 1’ ⇒ 30” = \(\frac{30}{60}\) = 0.5′ 

Now, we have 5° 37’30” = 5° 37.5’ 

We know that, 60’ = 1° 

⇒ 37.5’ = \(\frac{37.5}{60}\) = 0.625 

Now, we have 5° 37.55’ = 5.625° 

We know that 180° = π radian 

⇒ 5.625° = 0.03125π radian.