Fundamental Trig Identities

Question 1

Reciprocal Identities:

Answer 1

sin(x)= 1/csc(x)
cos(x)= 1/sec(x)
tan(x)= 1/cot(x)
csc(x)= 1/sin(x)
sec(x)= 1/cos(x)
cot(x)= 1/tan(x)

Question 2

Quotient Identities:

Answer 2

tan(x)= sin(x)/cos(x)
cot(x)= cos(x)/sin(x)

Question 3

Pythagorean Identities:

Answer 3

sin^2(x) + cos^2(x)= 1
1 + tan^2(x)= sec^2(x)
1 + cot^2(x)= csc^2(x)

Question 4

Cofunction Identities:

Answer 4

sin(pi/2 - x)= cos(x)
cos(pi/2 - x)= sin(x)
tan(pi/2 - x)= cot(x)
cot(pi/2 - x)= tan(x)
sec(pi/2 - x)= csc(x)
csc(pi/2 - x)= sec(x)

Question 5

Even and Odd Identities:

Answer 5

sin(-x)= -sin(x)
cos(-x)= cos(x)
tan(-x)= -tan(x)
csc(-x)= -csc(x)
sec(-x)= sec(x)
cot(-x)= -cot(x)