I'm doing a partial derivative series of the area (A) of a triangle. We have two sides (a and b) and the angle between them (C), and the area formula is A=a*(b*sin(C))/2. That would make a the base, and b*sin(C) should return the height, then base times height and divide by two because triangle. I'm starting from A=.5ab*sin(C) because I like that form better, and in this part of the series we're solving for dA/dC. When solving for a or b I left sin(C) alone, but since I'm now solving for C I believe I should be differentiating that to cos(C): dA/dC = .5ab*cos(C) I'm working with values a=111.27m, b=227.48m C=32Deg 18Min 34Sec or 32.30944444 I believe that means A=6764.446323m2 When I plug everything back in to dA/dC I get 10696.39132. If this is correct, then what is the operation using dA/dC that returns the original area 6764.446323? (To check my work.) If it's not correct, then what did I miss? And I'm being cautious because I did find solvers online that don't change sin(C) to cos even when solving for C -- they leave it as sin(C) -- which really surprised me.
I'm doing a partial derivative series of the area (A) of a triangle. We have two sides (a and b) and the angle between them (C), and the area formula is A=a*(b*sin(C))/2. That would make a the base, and b*sin(C) should return the height, then base times height and divide by two because triangle.
I'm starting from A=.5ab*sin(C) because I like that form better, and in this part of the series we're solving for dA/dC.
When solving for a or b I left sin(C) alone, but since I'm now solving for C I believe I should be
dA/dC = .5ab*cos(C)
I'm working with values a=111.27m, b=227.48m C=32Deg 18Min 34Sec or 32.30944444
I believe that means A=6764.446323m2
When I plug everything back in to dA/dC I get 10696.39132.
If this is correct, then what is the operation using dA/dC that returns the original area 6764.446323? (To check my work.) If it's not correct, then what did I miss? And I'm being cautious because I did find solvers online that don't change sin(C) to cos even when solving for C -- they leave it as sin(C) -- which really surprised me.
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