Inverse cosine with varriables

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Main Question or Discussion Point

Is there any equation or method that can be used in place of a trigonomic function when side values of a triangle are known only as varriables? For example: triangle abc where c is the center of a circle and AC and BC are radiui who's value = x, and AB = x-2y. So far as I know, the area of this sector (ACB) can be found in terms of x and y but must contain a trigonomic function of x and y as well. ( such as (cos-1( x..y/x..y))(pie.r^2) . Is there any way to know the area of this sector simply in values of x and y without a trigonomic function?
 

Answers and Replies

Tide
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Think of AB as the base the triangle. Use Pythagoras to determine the height of the triangle (draw a perpendicular from the center of the circle to the base - which bisects it!). Then you can write the area of the triangle (base X height / 2) in terms of x and y without the need for trig functions.
 
Fermat
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I did something like that as well with A = ½ab.sinC and the cosine rule, but it's the area of the sector, rather than of the triangle he wants.
 

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