Holiday Post 1

Triangle trigonometry:
sine = opp/hyp
cos = adj/hyp
tan = opp/adj
csc = hyp/opp
sec=hyp/adj
cot=adj/opp

Moving between quadrants:

I to IV = make it negative and add 360º
I to III = add 180º
I to II = make it negative and add 180º

II to IV = move 180º

Law of sines (sinA/a) = (sinB/b) = (sinC/c)
Law of cosines (opp leg)² = (other adj leg)² -2(adj leg) (adj Leg) cos (angle b/w)

sinΘ = y/r
cosΘ = x/r

tanΘ = y/x
cotΘ = x/y
cscΘ = r/y

secΘ = r/x

r=√(x² + y²) 

Graphing Trig functions:

y=Asin(Bx-h)+C

A = amplitude or height

B determines period(p)

p = (2π/B)

h = ((phase shift-horizontal shift)/(opposite))

C= vertical shift 

Trigonometric Identites:
csc = 1/sin x
sec = 1/cos x
cot x = 1/tan x
sin (-x) = -sin x
cos (-x) = cos x
csc (-x) = -csc x
sec (-x) = sec x
tan (-x) = -tan x
cot (-x) = -cot x
sin^2 x+cos^2 x = 1
1+tan^2 x = sec^2 x
1+cot^2 x = csc^2 x
sin x = cos(90*-x)
tan x = cot (90*-x)
sec x = csc (90*-x)
cos x = sin (90*-x)
cot x = tan (90*-x)
csc x = sec (90*-x)
tan x = sinx/cosx
cot x = cosx/sinx