Segmen of Circle Area

[nycmath]

Show your work in step by step fashion, preferably using the provided LaTex.

[Eigenvalue]

Method 1:

[Eigenvalue]

Method 2:

[Eigenvalue]

Note: the mathematical term for a fraction of a circle is "sector" rather than "segment". A segment is bound by an arc and a chord. The problem denotes a central angle and a radius, which implies that it pertains to a sector. I will post calculations for both a segment and a sector.

[nycmath]

Note: the mathematical term for a fraction of a circle is "sector" rather than "segment". A segment is bound by an arc and a chord. The problem denotes a central angle and a radius, which implies that it pertains to a sector. I will post calculations for both a segment and a sector.

I believe it is a typo on my part. I think the question should read find the area of the sector.

[nycmath]

Method 1:

An easier method for sure.

[nycmath]

Method 2:

Interesting.

[nycmath]

@Eigenvalue:

I appreciate all the effort you put into sharing the different methods to solve this problem. I think, however, that you should stick to the precalculus method(s) for two reasons:

A. We are on a precalculus journey through the Sullivan textbook.


B. Precalculus students in this forum have not taken linear algebra. They are not going to comprehend linear algebra methods at all.