AP Precalculus Trig Identities and Polar Graph Stuff

sin²x + cos²x =

1

1 + tan²x =

sec²x

1 + cot²x =

csc²x

sin(-u) =

-sin(u)

cos(-u) =

cos(u)

tan(-u) =

-tan(u)

csc(-u) =

-csc(u)

sec(-u) =

sec(u)

cot(-u) =

-cot(u)

sin(∏/2 - x) =

cos(x)

cos(∏/2 - x) =

sin(x)

tan(∏/2 - x) =

cot(x)

csc(∏/2 - x) =

sec(x)

sec(∏/2 - x) =

csc(x)

cot(∏/2 - x) =

tan(x)

sin(A + B) =

sinAcosB + cosAsinB

cos(A + B) =

cosAcosB - sinAsinB

tan(A + B) =

tanA + tanB/1 - tanAtanB

sin(A - B) =

sinAcosB - cosAsinB

cos(A - B) =

cosAcosB + sinAsinB

tan(A - B) =

tanA - tanB/1 + tanAtanB

sin(2A) =

2sinAcosA

cos(2A) =

cos²A - sin²A

2cos²A - 1

1 - 2sin²A

tan(2A) =

2tanA/1 - tan²A

sin(A/2) =

cos(A/2) =

tan(A/2) = given cosine

tan(A/2) = given both

tan(A/2) = also given both

r = acos(x)

r = asin(x)

circle

r = a ± bsin(x)

r = a ± bcos(x)

a/b < 1

inner loop limaçon

r = a ± bsin(x)

r = a ± bcos(x)

a/b = 1

cardioid

r = a ± bsin(x)

r = a ± bcos(x)

a/b is between 1 and 2

dimpled limaçon

r = a ± bsin(x)

r = a ± bcos(x)

a/b ≥ 2

no inner loop or dimple limaçon

r = asin(nx)

r = acos(nx)

rose curve

n is odd

petal number = n

n is even

petal number = 2n