The composite argument properties have sums of two angles or arcs. Similar properties for sums of three angles can be derived by first associating two of the angles. Write the expression in terms of SinA, sinB, SinC, cosA, cosB, and cosC.
sin (A + B + C)
Please help I need it for my Math Team thanks!
sin (A + B + C) = sin ((A + B) + C) = sin (A + B) cos C + cos (A + B) sin C
= cos C(sin A cos B + cos A sin B) + sin C(cos A cos B – sin A sin B)
= sin A cos B cos C + cos A sin B cos C + cos A cos B sin C – sin A sin B sin C
These use the two angle sum formulas:
sin (A + B) = sin A cos B + cos A sin B
cos (A + B) = cos A cos B – sin A sin B
sin (A + B + C) = sin ((A + B) + C) = sin (A + B) cos C + cos (A + B) sin C
= cos C(sin A cos B + cos A sin B) + sin C(cos A cos B – sin A sin B)
= sin A cos B cos C + cos A sin B cos C + cos A cos B sin C – sin A sin B sin C
These use the two angle sum formulas:
sin (A + B) = sin A cos B + cos A sin B
cos (A + B) = cos A cos B – sin A sin B
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