This radian question is confusing me (1 Viewer)

[Dragonmaster262]

Find the area of the minor segment of a circle with a radius of 2.1 m and with an angle subtended is

I put my calculator in radians and then use the formula

The answer is supposed to be 0.99 m^2. Anybody know what I did wrong?

 

[Top Secret]

is degrees. Put your calculator in degree mode, and try again.

 

[Dragonmaster262]

i did that and the answer came out as 179.91. The answer is supposed to be 0.99.

 

[Top Secret]

I see your mistake.

I your equation, you say the area of the sector is:

0.5 x 2.1squared x 82degrees.

It should be:

(0.5 x 2.1squared x 82degrees) x pie / 180

 

[Drongoski]

i did that and the answer came out as 179.91. The answer is supposed to be 0.99.

82 deg 35 min = 82 7/12 deg = 82.583333 deg = (82.58333 x pi)/180 radians = 1.44135 . . . radians

.: area of segment = 0.5 x 2.1 x 2.1 (1.44135 .. - sin 1.44135 ..) = 0.99162 .. m²

 

[Top Secret]

82 deg 35 min = 82 7/12 deg = 82.583333 deg = (82.58333 x pi)/180 radians = 1.44135 . . . radians

.: area of segment = 0.5 x 2.1 x 2.1 (1.44135 .. - sin 1.44135 ..) = 0.99162 .. m²

Dragonmaster262, make sure you set your calculator back to radians before testing this out.

 

[Dragonmaster262]

I have trouble converting angles to radians. By converting 82'35 you multiply it with pi/180 and it comes out with the right answer but suppose you want to convert 30 to radians. If you multiply it to pi/180 you get the wrong answer. Is there any specific rule of when and where to use pi/180.

 

[Drongoski]

I have trouble converting angles to radians. By converting 82'35 you multiply it with pi/180 and it comes out with the right answer but suppose you want to convert 30 to radians. If you multiply it to pi/180 you get the wrong answer. Is there any specific rule of when and where to use pi/180.

Angle size can be expressed in 2 different units; just as temperature can be expressed in degrees F or C among others.

For angles: just remember the angle of 1 full revolution you know as 360 degrees is 2 pi radians. so if you have angle of 30 degrees, this is 30/360 = 1/12 of a revolution = 1/12 of 2 pi = pi/6 radians [you can get it equivalently by: 30 x pi/180]

Shouldn't be too hard.

 

[gurmies]

I have trouble converting angles to radians. By converting 82'35 you multiply it with pi/180 and it comes out with the right answer but suppose you want to convert 30 to radians. If you multiply it to pi/180 you get the wrong answer. Is there any specific rule of when and where to use pi/180.

30 x pi/180 = pi/6

 

[mwatts]

easy way to remember how to convert between is that
radians usually has a fraction of pi therefore you times by pi/180
degrees has no pi therfore you divide by 180/pi

 

[Drongoski]

and pi/6 = 3.14159 ... / 6 = 0.523598 ... ( radians)

Another way of having a feel for radians: 1 radian is approx 57.3 degrees

 

[Dragonmaster262]

Ok thanks guys.

 

[gurmies]

Ok thanks guys.

If ever in doubt, do what I do and take ratios:

180 degrees = pi radians

30 degrees = x radians

Cross multiply

180x = 30pi

x = pi/6 radians.