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Level 486

Precalculus


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f(x)=mx+b
linear function
f(x)=mx
direct variation
quadratic
f(x)=ax²+bx+c or f(x)=a(x-h)² +k
-f(x)
reflection over x-axis (y-coordinates become opposite)
f(-x)
reflection over y-axis (x-coordinates become opposite)
|f(x)|
above x-axis stays the same, below x-axis reflects over the x-axis
f|(x)|
right of y-axis stays the same, left of y-axis reflection right of y-axis
sine
sinx= Opp/Hyp=y/r
Cosine
cosx=Adj/Hyp=x/r
Tangent
tanx=Opp/Adj=y/x
cosecant
cscx=Hyp/Opp=r/y
secant
secx=Hyp/Adj=r/y
cotangent
cotx=Adj/Opp=x/y
reciprocal properties
sinx=1/cscx cscx=1/sinx
tanx=sinx/cosx=secx/cscx
quotient properties
cos²x+sin²x=1
Pythagorean properties
angle locations:
for inverse sine, cosecant, tangent, cotangent angle goes in I Quad if positive and IV Quad if negative
angle locations:
for inverse cosine, secant angle goes in I Quad if positive and II Quad if negative
Bcosx+Csinx=Acos(x-D) where
linear combination of cosine and sine with equal periods
cos(A-B)=cosAcosB+sinAsinB
composite argument properties
f(x)=f(-x)
even function
-f(x)=f(-x)
odd function
sin⊗=cos(90°-⊗)
co-function properties
sin(2A)=2sinAcosA
double argument properties
sin½A=±√(½(1-cosA))
half argument properties
sinxcosx=½sin2x
products & squares of cosine & sine