Question

Radian measure of 39°22'30'' is?​

Answer 1

Ans will be

$7π/32 Radians$

Given in the question :

$39\: degree\: 22\: minutes 30\: seconds$

$39°22'30"$

First we will convert the question into one unit and then we will convert it to radians.

$1 degree = 60 minutes$

$1' minute= 60 seconds$

So

$30 seconds = 1/2 minutes$

Our question becomes

$39° 22+1/2'$

$39° 45/2'$

$39 \:degree 45/2 \:minutes$

Now we will convert the whole to degree to get a single unit.

As 1° = 60 minutes

$45/2'=45/2×1/60°$

$=3/8 degree$

Thus our question:

$39+3/8°$

$= 315/8°$

So the question is converted to a single unit.

Now we have to convert 315/8° to radians

$1\: degree = π /180\: radian$

$315/8°\:= 315/8×π/180$

$= 7π/32\: Radians$

$our\: answer$

Why we need radians?

Radians are dimensionless. They can be treated just as numbers .

They were originally put to use to relate the angle to the radius of the circle.

Almost all rotational motion equation uses radians instead of measuring angle in degree.

The use of Radians for the first time is credited to Roger Cotes in 1714.

Further links-

https://www.google.com/url?sa=t&source=web&rct=j&url=https://brainly.in/question/4241626&ved=2ahUKEwiF-tqy-dr5AhUTzzgGHZ2bDcwQjjh6BAgNEAE&usg=AOvVaw13Wxm8F-Ag36Pxmx0w-f9y

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Answer 2

Answer:

The radian measure of 39°22'30'' is 0.6872 Rad.

Step-by-step explanation:

There are three units of angle measurements.

1. Gradians
2. Degrees
3. Radians

• A gradian is a one-hundredth of a right angle (90°). A full circle or 2π radians is equal to 400 grads.
• A degree is a 1/$360^{th}$ of a circle. It is the most widely used measuring system.
• A radian is an angle subtended from the center of a circle that intercepts an arc equal to the radius of circle.

A degree can be further divided into minutes.

1° = 60'

A minute can be further divided into seconds.

1' = 60"

Also, degrees and radians can be converted from each other using the relation 2π radians = 360°.

Given 39°22'30'' to be converted into radians.

Calculation:

Converting the minutes and seconds into degrees.

22'/60' = 0.36666°

30"/3600" = 0.00833°

39°22'30'' in Degrees is 39 + 0.36666+ 0.00833 = 39.375°

Converting degrees into radians:

39.375 * π/180 = 0.6875 Rad

Know more about angle conversions:

Convert radians to degrees

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Find the degree measures corresponding to the following radian measures (Use π = 22/7)

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