...cos B — sin A sin B sin C cos A cos B cos C — cos A sin B sin C — cos B sin A sin C — cos C sin A sin B Dividing both numerator and denominator by cos A cos B cos C, we find tf A 4- B -4- fl - • 1 + * ' ; ~ 1 - tan A tan B - tan A tan C -tan B tan'C If C =...

...sine and cosine : . , AP\ — sin (A - B) — sin A cos B — cos A sin B cos (A — B) cos A cos B+ sin A sin B Dividing both numerator and denominator by cos A cos B gives tanM-g) = tan4-tang (2Q) l + t&nAt&nB' which expresses tan (A — B) in terms of tangents only....

...angles, presented here somewhat abbreviated, are the sine and cosine formulas: and sin(/4 - B) = sin A cos B - cos A sin B cos(A - B) = cos A cos B + sin A sin B 90° -A Geometrical Construction Quadrant Angle + Sine Cosine Tangent 1st A + + = + + T - + +...

...sin2* + cos2* = 1, sin* tan* = cos* 1 cot* = tan* addition and subtraction formulas: sin(a ± b) = sin a cos b ± cos a sin b, cos(a ± b) = cos a cos b ^ sin a sin b, tan a ± tan b tan (a ± b) = -; double-angle formulas: sin2a = 2 sin a cosa, cos 2a = 2 cos2...

...A*2) + r2 sin(*, + A*,) - r4 sin(d,4 + A,£4) = 0 Using the trigonometric identities sin(a + b) = sin a cos b + cos a sin b, cos(a + b) = cos a cos b - sin a sin b and that for small angles Aa, sin Aa ~ Aa. cos Aa ~ 1, we obtain from Equation (2.10a) and (b):...

...cos2 x — 1, sinx tanx = cotx = cos x 1 tanx addition and subtraction formulas: sin(a ± b) = sin a cos b ± cos a sin b, cos(a ±b) = cos a cos b =p sin a sin b, , , tan a ± tan b tan(a ± 6) = ; 1 ^ tan a tan b double-angle formulas: sin2a = 2...

...all angles A and B (24) (25) (26) (27) sm(A + B) — sin A cos B + cos A sin B , sin(A — B) — sin A cos B — cos A sin B , cos(A + B) = cos A cos B — sin A sin B , cos(A — B) = cos A cos B + sin A sin B . Clearly Equation (27) is the formula that replaces...

...of square roots must be chosen appropriately in other quadrants. Addition formulae sm(A ± B) - sin A cos B ± cos A sin B cos(A ± B) = cos A cos B + sin A sin ß tan A ± tan ß lan(A ± B) - — — l -t- tan A tan B Sum and difference formulae sin A +...

...of square roots must be chosen appropriately in other quadrants. Addition formulae sin(A + B) = sin A cos B + cos A sin B cos(A ± B) = cos A cos B + sin tan A + tan tan(A + B) = -—- sin 1 + tan A tan 5 Sum and difference formulae sin A + sin 5 = 2 sin...

...formulae The basic compound angle formulae are: sin(A + B) = sin A cos B + cos A sin B sin(A — B) = sin A cos B — cos A sin B cos(A + B) = cos A cos 5 — sin A sin B cos(A — B) = cos A cos 5 + sin A sin B tan A + tan B tan (A + B) = tan (A - B)...