Precalculus Sem 1 Formula Sheet
Formulas
Slope formula
m = (y2 – y1)/(x2 – x1)
Point-Slope formula
y – y1 = m(x – x1)
Quadratic Formula
𝑥𝑥 =
−𝑏𝑏±√𝑏𝑏2 −4𝑎𝑎𝑎𝑎
2𝑎𝑎
Compound Interest
Exponential Growth/Decay
y = Cax (a > 0, a ≠ 1)
Continuously Compounded Interest
N = N0(1 + r)t
or
N= N0ekt
or
A = Pert
Pythagorean Theorem x2 + y2 = r2
Distance Formula
Standard Form Equation of a Circle
(x − h)2 + (y − k)2 = r 2
Standard Form Equation of a Quadratic Function
Vertex Form Equation of a Parabola
y = ax2 + bx + c
y = a(x − h)2 + k or x = a(y − k)2 + h
Parabola
a ( x − h ) =( y − k ) where a =
2
Focus: ( h, k ± c )
1
4c
a ( y − k ) =( x − h) where a =
2
Focus: ( h ± c, k )
Directrix: x= h ± c
Directrix: y= k ± c
Standard Form Equation of an Ellipse
, c2 =a2-b2
or
Ellipses
( x − h)
a2
2
(y −k)
+
b2
1
4c
2
=
1
( x − h)
b2
2
(y −k)
+
a2
2
=
1
2
a, b, c relationship: c=
a 2 − b2
Foci: ( h ± c, k )
2
a, b, c relationship: c=
a 2 − b2
Foci: ( h, k ± c )
Major axis vertices: ( h ± a, k )
Major axis vertices: ( h, k ± a )
Minor axis vertices: ( h, k ± b )
Minor axis vertices: ( h ± b, k )
Standard Form Equation of a Hyperbola
Hyperbolas
( x − h)
a2
2
(y −k)
−
2
b2
1
=
(𝑥𝑥−ℎ)2
𝑎𝑎 2
−
(𝑦𝑦−𝑘𝑘)2
𝑏𝑏2
= 1 or
(y −k)
a2
2
(𝑦𝑦−𝑘𝑘)2
𝑎𝑎 2
−
( x − h)
−
(𝑥𝑥−ℎ)2
𝑏𝑏2
= 1, c2 =a2+b2
2
b2
=
1
2
a, b, c relationship: c=
a 2 + b2
Foci: ( h ± c, k )
2
a, b, c relationship: c=
a 2 + b2
Foci: ( h, k ± c )
Vertices: ( h ± a, k )
Vertices: ( h, k ± a )
b
a
± ( x − h) + k
Asymptotes: y =
Rotation Equations x = x' cos
+ y' sin
a
b
± ( x − h) + k
Asymptotes: y =
and y = -x' sin
+ y' cos
Fundamental Trigonometric Identities
Reciprocal Identities cscx=1/sinx
secx=1/cosx
Quotient Identities
cotx=cosx/sinx
tanx=sinx/cosx
cotx=1/tanx
Identities for Negatives
sin(−x)=−sinx
cos(−x)=cosx
tan(−x)=−tanx
Pythagorean Identities
sin2x+cos2x=1
1+tan2x=sec2x
1+cot2x=csc2x
Sum Identities
sin(A+B)=sinAcosB+cosAsinB
cos(A+B)=cosAcosB−sinAsinB
tan(A+B)=(tanA+tanB) / (1−tanAtanB)
Difference Identities
sin(A−B)=sinAcosB−cosAsinB
cos(A−B)=cosAcosB+sinAsinB
tan(A−B)=(tanA−tanB)/(1+tanAtanB)
Double Angle Identities
sin2a=2sinacosa
cos2a =cos2a−sin2a
=2cos2a−1
=1−2sin2a
tan2a=(2tan a)/(1−tan2a)
Power Reducing Identities
Half Angle Identities