Stephanie's Reflection

Sine and Cosine Sum/Difference Formulas:
cos(alpha+/-beta)=cos alpha cos beta-/+sin alpha sin beta )
sin(alpha+/- beta)=sin alpha cos beta +/-cos alpha sin beta
sin x+sin y=2sin(x+y/2)cos(x-y/2)
sin x-sin y=2cos(x+y/2)sin(x-y/2)
cos x+cos y= 2cos(x+y/2)cos(x-y/2)
cos x-cos y=-2sin(x+y/2)sin(x-y/2)

Tangent Sum/Difference Formulas:
tan(alpha+beta)=tan alpha+tan beta/1-tan alpha tan beta
tan alpha-beta=tan alpha-tan beta/1+tan alpha tan beta

Double-Angle/Half-Angle Formulas:
sin 2α=2sinα cosα
cos 2α=cos2α-sin2α=1-2sin2α=2cos2α-1
tan 2α=2tanα/1-tan2α
sin(α/2)=+/-√(1-cosα/2) cos(α/2)= +/-√(1+cosα/2)
tan(α/2)= +/-√(1-cosα/1+cosα)=sinα/1+cosα= 1-cosα/sinα)

sin=y/r
cos=x/r
tan=y/x
cot=x/y
sec=r/x
csc=r/y


Trig Chart:
0°
sin0=0
cos0=1
tan0=undefined
sec0=1
cot0=0
30°
sinπ/6=1/2
cosπ/6=√3/2
tanπ/6=√3/3
cscπ/6=2
secπ/6=2 √3/3
cotπ/6=√3
45°
sinπ/4=√2/2
cosπ/4=√2/2
tanπ/4=1
cscπ/4=√2
secπ/4=√2
cotπ/4=1
60°
sinπ/3=√3/2
cosπ/3=1/2
tanπ/3=√3
cscπ/3=2 √3/3
secπ/3=2
cotπ/3=√3/2
90°
sinπ/2=1
cosπ/2=0
tanπ/2=undefined
cscπ/2=1
secπ/2=undefined
cotπ/2=0

Reciprocal Relationships:
cscΘ=1/sinΘ
secΘ=1/cosΘ
cotΘ=1/tanΘ

Relationships with Negatives:
sin -Θ= -sinΘ and cos -Θ= -cosΘ
csc -Θ= -cscΘ and sec -Θ= -secΘ
Tan -Θ= -tanΘ and cot -Θ= -cotΘ

Pythagorean Relationships:
sin²Θ+cos²Θ=1
1+tan²Θ=sec²Θ
1+cot²Θ=csc²Θ

Cofunction Relationships:
sinΘ=cos(90°-Θ) and cosΘ=sin(90°-Θ)
tanΘ=cot(90°-Θ) and cotΘ=tan(90°-Θ)
secΘ=csc(90°-Θ) and cscΘ=sec(90°-Θ)