Trig Identities

Question 0

Opposites theorem

Answer 0

For every A,
-sin(A)=sin(-A)
cos(A)=cos(-A)
-tan(A)=tan(-A)

Question 1

Pythagorean identity

Answer 1

(cosA)2+(sinA)2=1

Question 2

Supplements theorem

Answer 2

For every A,
sin(~-A)=sin(A)
cos(~-A)=-cos(A)
tan(~-A)=-tan(A)

Question 3

Complements theorem

Answer 3

For every A,
sin((~/2)-A)=cos(A)
cos((~/2)-A)=sin(A)

Question 4

Addition identity for sine

Answer 4

sin(A+B)=sin(A)cos(B)+cos(A)sin(B)

Question 5

Addition identity for cosine

Answer 5

cos(A+B)=cos(A)cos(B)-sin(A)sin(B)

Question 6

Subtraction identity for cosine

Answer 6

cos(A-B)=cos(A)cos(-B)-sin(A)sin(-B)

Question 7

Subtraction identity for sine

Answer 7

sin(A+B)=sin(A)cos(B)-cos(A)sin(B)

Question 8

Double angle identity for sine

Answer 8

sin2A=2sinAcosA

Question 9

Double angle identities for cosine

Answer 9

cos2A=cos(sq)A-sin(sq)A
cos2A=2cos(sq)A-1
cos2A=1-2sin(sq)A