free notes for precalc wheee

didn't had the time to grind amc yesterday bc school math test coming up :sob:
goal: 1-2 amcs today + do p1-6 on 2010 aime (lol at this rate I'm failing aime)

currently reading precalc textbook
chapter 7.1-7.5
trig identities

identities to remember:
- trig addition
sin(x+y) = sinxcosy+cosxsiny
sin(x-y) = sinxcosy-cosxsiny
cos(x+y) = cosxcosy-sinxsiny
cos(x-y) = cosxcosy+sinxsiny
tan(x+y) = (tanx+tany)/(1-tanxtany)
tan(x-y) = (tanx-tany)/(1+tanxtany)

- double angle
sin2x = 2sinxcosx
cos2x = cos²x-sin²x = 2cos²x-1=1-sin²x
tan2x = sin2x/cos2x = 2tanx/(1-tan²x)

- half angle
sin(x/2) = ±√((1-cosx)/2) - CHECK QUADRANT
cos(x/2) = ±√((1+cosx)/2) - CHECK QUADRANT
tan(x/2) = (1-cosx)/sinx = sinx/(1+cosx)

- power reduce
sin²x = (1-cos2x)/2
cos²x = (1+cos2x)/2
tan²x = (1-cos2x)/(1+cos2x)

life summary:
finished all parent-teacher-student conferences yesterday and they all went well enough ig
most (if not all) of the teachers said I'm a good student
which is nice of them for such a praise

I touched ipad yesterday too
and redrew a piece from back in march
turned out better than expected
took me like 3 hours lol but at least I can draw backgrounds
still can't draw clothes tho so I need to practice that

original piece of art

I drew two different backgrounds, and they gave out different feels
#1
#2

- helena