How does multiplying cosA by its inverse isolate A?

Question

Cos does not have any numerical meaning by itself, but cosA has a distinct value. If we multiply that value by its inverse, I can understand how we produce an answer of one. But how does that process isolate the variable A?

 

Thanks.

 

Cary

Answer 1

The way to extract A from cosA is to use cosA as the input to the arccos or cos^-1 function.

arccos(cosA)=A or cos^-1(cosA)=A.  This needs to be modified since cosA = cos(2π-A)

Answer 2

Cary, you're right that "cosine" by itself doesn't have a numerical value. Calculating the cosine is something you do TO a number, depending on what other information you have (specifically ratios).

 

Suppose the cosine of an angle A in a triangle is 4/5;

 

so 4/5A x 5/4 (the inverse) gives you A--all alone, isolated.

 

See how that works?

 

Hope this is helpful.

 

Matt in New York