## 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)**

**i³**

**-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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