Trigonometry Final Study Guide

Finding area of a triangle given SAS
K=1/2bcsinA: b and c-given sides, A-angle between two sides

one period of sin θ
(360°)hits x axis at 0°, 180°, and 360°

one period of cos θ
(360°)hits x axis at 90° and 270°

one period of tan θ
(180°)backwards s curve(first up second down), first asymptote at 90°, hits x axis at 0° and 180°

one period of csc θ
(360°)flip arches from sine, never hits the x axis, asymptotes at 0°, 180°, and 360°

one period of sec θ
(360°)flip arches from cosine, never hits the x axis, asymptotes at 90° and 270°

one period of cot θ
(180°) forms s curve, hits x axis at 90°, asymptotes at 0° and 180°

SSA Ambiguous Case
If a=bsinA then 1∆, if absinA then a≥b 1∆ or a

Hero’s formula
used when given SSS and asked for area:K=√s(s-a)(s-b)(s-c) where s=1/2(a+b+c)

finding area when given SSS of a triangle
K=1/2bcsinA

equation for trig graphs
f(x)=asinb(x-h)+k

|a| in trig graph equation
amplitude:>1=vertical stretch, <1=vertical compression, if negative graph is flipped

b in trig graph equation
2π/b=period for sin, cos, csc, sec, π/b=period for tan, cot

h in trig graph equation
horizontal shift:+=left, -=right

k in trig graph equation
vertical shift:+=up, -=down

intervals when graphing trig equations
1/4period

sin 2θ
2sinθcosθ

sin(α±β)
sinαcosβ±cosαsinβ

cos(α+-β)
cosαcosβ−+sinαsinβ

cos 2θ
cos²θ-sin²θ

tan 2θ
2tanθ/1-tan²θ

opposite
-z(straight across from angle)

conjugate
z with line over it(mirror image of angle)

reciprocal
z⁻¹(mirrored and flipped r of angle)

-i

i⁴
1

regular circle
r=4sinθ

rose
r=2sin2θ, first 2:length of petals, second 2:number of petals but is even so must be doubled

limacon w/ inner loop
r=1-2cosθ

limacon w/o inner loop
r=3+2cosθ

cardioid
r=2+2sinθ

determining classical curve
r=a+bcos/sineθ:|a|=|b|→cardioid, |a|<|b|→limacon w/ inner loop, |a|>|b|→limacon w/o inner loop

lemniscate
r²=4cos2θ

r²=
x²+y²

tan(α+β)
tanα+tanβ/1-tanαtanβ

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