AP-Precalculus Identities

sin²x+cos²x

=1

1+tan²x

=sec²x

1+cot²x

=csc²x

sin(A+B)

=sinAcosB+cosAsinB

sin(A-B)

=sinAcosB-cosAsinB

cos(A+B)

=cosAcosB-sinAsinB

cos(A-B)

=cosAcosB+sinAsinB

sin(2x)

=2sinxcosx

cos(2x)

=cos²x-sin²x

=2cos²x-1

=1-2sin²x

Log_b(1)

=0

Log_b(b)

=1

Log_b(b^y)

=y

b^log_b(x)

=x

Log_b(x)=y

b^y=x

For f(x)=ax^n/bx^d

If: n=d Then:

HA is at y=a/b

For f(x)=ax^n/bx^d

If: n<d then:

HA is at Y=0

For f(x)=ax^n/bx^d

If: n>d Then:

No HA

For f(x)=ax^n/bx^d

If: n is one more than d Then:

There is a slant asymptote

And even function is when

f(-x)=f(x)

An odd function is when

f(-x)=-f(x)

Rectangular to Polar coordinates

x²+y²=r²

tan(theta)=y/x

Polar to Rectangular coordinates

x=rcos(theta)

y=rsin(theta)

limacon

f(theta)=a+bsin(theta)

f(theta)=a+bcos(theta)

Inner loop limacon

f(theta)=a+bsin(theta)

f(theta)=a+bcos(theta)

When a/b<1 (the length of the inner loop is a-b)

Cardioid limacon

f(theta)=a+bsin(theta)

f(theta)=a+bcos(theta)

When a/b=1 (a+b is the max distance)

Dimpled limacon

f(theta)=a+bsin(theta)

f(theta)=a+bcos(theta)

When 1<a/b<2 (max distance is a+b; min distance is a-b)

No dimple no loop limacon

f(theta)=a+bsin(theta)

f(theta)=a+bcos(theta)

When a/b>=2