Tài liệu

Appendix

Mathematics and Statistics

Graphs of the Parent Functions

Graphs of the Trigonometric Functions

Trigonometric Identities

Pythagorean Identities cos 2 t+ sin 2 t=1 1+ tan 2 t= sec 2 t 1+ cot 2 t= csc 2 t
Even-Odd Identities cos(−t)=cost sec(−t)=sect sin(−t)=sint tan(−t)=tant csc(−t)=csct cot(−t)=cott
Cofunction Identities cost=sin( π 2 t ) sint=cos( π 2 t ) tant=cot( π 2 t ) cott=tan( π 2 t ) sect=csc( π 2 t ) csct=sec( π 2 t )
Fundamental Identities tant= sint cost sect= 1 cost csct= 1 sint cott= 1 tant = cost sint
Sum and Difference Identities cos(α+β)=cosαcosβsinαsinβ cos(αβ)=cosαcosβ+sinαsinβ sin(α+β)=sinαcosβ+cosαsinβ sin(αβ)=sinαcosβcosαsinβ tan(α+β)= tanα+tanβ 1tanαtanβ tan(αβ)= tanαtanβ 1+tanαtanβ
Double-Angle Formulas sin(2θ)=2sinθcosθ cos(2θ)= cos 2 θ sin 2 θ cos(2θ)=12 sin 2 θ cos(2θ)=2 cos 2 θ1 tan(2θ)= 2tanθ 1 tan 2 θ
Half-Angle Formulas sin α 2 =± 1cosα 2 cos α 2 =± 1+cosα 2 tan α 2 =± 1cosα 1+cosα tan α 2 = sinα 1+cosα tan α 2 = 1cosα sinα
Reduction Formulas sin 2 θ= 1cos( 2θ ) 2 cos 2 θ= 1+cos( 2θ ) 2 tan 2 θ= 1cos( 2θ ) 1+cos( 2θ )
Product-to-Sum Formulas cosαcosβ= 1 2 [ cos(αβ)+cos(α+β) ] sinαcosβ= 1 2 [ sin(α+β)+sin(αβ) ] sinαsinβ= 1 2 [ cos(αβ)cos(α+β) ] cosαsinβ= 1 2 [ sin(α+β)sin(αβ) ]
Sum-to-Product Formulas sinα+sinβ=2sin( α+β 2 )cos( αβ 2 ) sinαsinβ=2sin( αβ 2 )cos( α+β 2 ) cosαcosβ=2sin( α+β 2 )sin( αβ 2 ) cosα+cosβ=2cos( α+β 2 )cos( αβ 2 )
Law of Sines sinα a = sinβ b = sinγ c a sinα = b sinβ = c sinγ
Law of Cosines a 2 = b 2 + c 2 2bccosα b 2 = a 2 + c 2 2accosβ c 2 = a 2 + b 2 2abcosγ
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