Summary In short maths.

FORMULA SHEET
MATH 1060-004 Trigonometry


The following formulas will be provided on the Final Test.

Sum and Difference Formula

sin( A + B) = sin A cos B + cos A sin B Sum to Product

sin( A − B) = sin A cos B − cos A sin B A±B A∓B
sin A ± sin B = 2 sin( ) cos( )
2 2
cos( A + B) = cos A cos B − sin A sin B
A+B A−B
cos( A − B) = cos A cos B + sin A sin B cos A − cos B = −2 sin( ) sin( )
2 2
tan A + tan B A+B A−B
tan( A + B) = cos A + cos B = 2 cos( ) cos( )
1 − tan A tan B 2 2
tan A − tan B
tan( A − B) =
1 + tan A tan B
Area of a Triangle

1 1
Double Angle Formula Area = ab sin C = bc sin A
2 2
q
1
sin(2A) = 2 sin A cos A = ac sin B = s(s − a)(s − b)(s − c)
2
cos(2A) = cos2 A − sin2 A a+b+c
where s = 2
cos(2A) = 2 cos A − 1 = 1 − 2 sin A
2 2
Law of Sines
2 tan A
tan(2A) =
1 − tan2 A a
=
b
=
c
sin A sin B sin C

Half Angle Formula
r Law of Cosines
A 1 − cos( A)
sin( ) = ± b2 + c2 − a2
2 2 cos A =
r 2bc
A 1 + cos( A)
cos( ) = ± a2 + c2 − b2
2 2 cos B =
2ac
A 1 − cos A sin A
tan( ) = = a2 + b2 − c2
2 sin A 1 + cos A cos C =
2ab

Product to Sum
Vectors
1 −
→v .−
→u
cos A cos B = (cos( A + B) + cos( A − B)) cos θ = −
2 k v kk−
→ →uk
1 −
→u .−
→
sin A sin B = (cos( A − B) − cos( A + B)) Proj−
→
−→ v −
→
v u = − → v
2 k v k2
1
sin A cos B = (sin( A + B) + sin( A − B)) → −−→
−
2 Work = F .disp




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