Trigonometry Final Study Guide – Flashcards
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Finding area of a triangle given SAS
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K=1/2bcsinA: b and c-given sides, A-angle between two sides
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one period of sin θ
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(360°)hits x axis at 0°, 180°, and 360°
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one period of cos θ
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(360°)hits x axis at 90° and 270°
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one period of tan θ
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(180°)backwards s curve(first up second down), first asymptote at 90°, hits x axis at 0° and 180°
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one period of csc θ
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(360°)flip arches from sine, never hits the x axis, asymptotes at 0°, 180°, and 360°
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one period of sec θ
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(360°)flip arches from cosine, never hits the x axis, asymptotes at 90° and 270°
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one period of cot θ
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(180°) forms s curve, hits x axis at 90°, asymptotes at 0° and 180°
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SSA Ambiguous Case
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If a=bsinA then 1∆, if absinA then a≥b 1∆ or a<b 2∆s
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Hero's formula
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used when given SSS and asked for area:K=√s(s-a)(s-b)(s-c) where s=1/2(a+b+c)
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finding area when given SSS of a triangle
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K=1/2bcsinA
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equation for trig graphs
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f(x)=asinb(x-h)+k
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|a| in trig graph equation
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amplitude:>1=vertical stretch, <1=vertical compression, if negative graph is flipped
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b in trig graph equation
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2π/b=period for sin, cos, csc, sec, π/b=period for tan, cot
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h in trig graph equation
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horizontal shift:+=left, -=right
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k in trig graph equation
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vertical shift:+=up, -=down
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intervals when graphing trig equations
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1/4period
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sin 2θ
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2sinθcosθ
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sin(α±β)
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sinαcosβ±cosαsinβ
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cos(α+-β)
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cosαcosβ−+sinαsinβ
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cos 2θ
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cos²θ-sin²θ
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tan 2θ
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2tanθ/1-tan²θ
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opposite
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-z(straight across from angle)
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conjugate
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z with line over it(mirror image of angle)
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reciprocal
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z⁻¹(mirrored and flipped r of angle)
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i³
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-i
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i⁴
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1
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regular circle
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r=4sinθ
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rose
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r=2sin2θ, first 2:length of petals, second 2:number of petals but is even so must be doubled
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limacon w/ inner loop
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r=1-2cosθ
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limacon w/o inner loop
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r=3+2cosθ
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cardioid
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r=2+2sinθ
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determining classical curve
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r=a+bcos/sineθ:|a|=|b|→cardioid, |a||b|→limacon w/o inner loop
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lemniscate
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r²=4cos2θ
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r²=
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x²+y²
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tan(α+β)
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tanα+tanβ/1-tanαtanβ
