TRIGONOMETRY ทั้งหมดเกิดจาก สามเหลี่ยมมุมฉากดังนี้
1.sin q = y/r
2.cos θ = x/r
3.tan θ = y/x,
4.cot θ = x/y
5.csc θ = r/y
6.sec θ = r/x
กฏของ sines
a/sineA = b/sineB = c/sineC
กฏของ Cosines
a2 = b2 + c2 - 2bccosA
b2 = a2 + c2 - 2accosB
c2 = a2 + b2 - 2bccosC
คุณสมบัติต่างๆ
- csc θ = 1/sin θ
- sec θ = 1/cos θ
- tan θ = sin θ/cos θ
- cot θ = 1/tan θ
- sineθ2 + cosθ2 = 1
- tanθ2 + 1 = secθ2
- cotθ2 + 1 = cscθ2
- sin (α + β) = sin α cos β + cos α sin β
- cos (α + β) = cos α cos β – sin α sin β
- sin 2α = 2 sin α cos α
- cos 2α = cos2α – sin2α = 1 – 2 sin2α = 2 cos2α – 1
- tan 2α = (2 tan α)/(1 – tan2α)
- cot 2α = (cot2α – 1)/(2 cot α)
- tan (α + β) = (tan α + tan β)/(1 – tan α tan β)
- cot (α + β) = (cot α cot β – 1)/(cot α + cot β)
- sin (α – β) = sin α cos β – cos α sin β
- cos (α – β) = cos α cos β + sin α sin β
- tan (α – β) = (tan α – tan β)/(1 + tan α tan β)
- cot (α – β) = (cot α cot β + 1)/(cot β – cot α)
- sin (α/2) = ±sqr((1− cos α)/2)
- cos (α/2) = ±sqr((1+ cos α)/2)
- tan (α/2) = ±sqr((1− cos α)(1+ cos α))
- cot (α/2) = ±sqr((1+ cos α)(1− cos α))
- sin α sin β = (1/2)[cos (α – β) – cos (α + β)]
- cos α cos β = (1/2)[cos (α – β) + cos (α + β)]
- sin α cos β = (1/2)[sin (α + β) + sin (α – β)]
- sin α + sin β = 2 sin (1/2)(α + β) cos (1/2)(α – β)
- sin α – sin β = 2 cos (1/2)(α + β) sin (1/2)(α – β)
- cos α + cos β = 2 cos (1/2)(α + β) cos (1/2)(α – β)
- cos α – cos β = – 2 sin (1/2)(α + β) sin (1/2)(α – β)
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