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# If angle A+angle B +angle C = (180 degrees) ,-A=B+C

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If angle A+angle B +angle C = $${\mathtt{\pi}}$$ (180 degrees) ,$${\mathtt{\pi}}$$-A=B+C

then sinA=sin($${\mathtt{\pi}}$$-A)=sin(B+C)

but A might not equal to B+C, right?

Guest Feb 4, 2015

#2
+91919
+5

Mmm

$$\\\pi-A=B+C\;\rightarrow\;A=\pi-(B+C)\\ or\\ A=B+C$$

But I can add 2pi*n to these answers where n is an integer

$$\\A=\pi-(B+C)+2n\pi=(2n+1)\pi-(B+C)\\ or\\ A=B+C +2n\pi$$

Mmm

$$\\A=(2n+1)\pi-(B+C)\\ or\\ A=2n\pi+(B+C)\\\\\\\\ I think the general formula for this would be\\ A=(-1)^n(B+C)+n\pi$$

I think that is right but I really need another mathematician to check my working.  :))

Melody  Feb 4, 2015
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#1
+752
+3

A+B+C = Pi

B + C    =  Pi - A

cos(B +C)= cos (Pi -A)

cos (B+C) = -(cos A)

-(cos A) = cos(-A)

so that,

cos(B +C)   = cos(-A)

now we cut cos

B+C    = -A//

Sasini  Feb 4, 2015
#2
+91919
+5

Mmm

$$\\\pi-A=B+C\;\rightarrow\;A=\pi-(B+C)\\ or\\ A=B+C$$

But I can add 2pi*n to these answers where n is an integer

$$\\A=\pi-(B+C)+2n\pi=(2n+1)\pi-(B+C)\\ or\\ A=B+C +2n\pi$$

Mmm

$$\\A=(2n+1)\pi-(B+C)\\ or\\ A=2n\pi+(B+C)\\\\\\\\ I think the general formula for this would be\\ A=(-1)^n(B+C)+n\pi$$

I think that is right but I really need another mathematician to check my working.  :))

Melody  Feb 4, 2015

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