Fundamental Trigonometric Identities

Front 1

Reciprocal Identities

Back 1

1. sin u = 1/csc u
2. cos u = 1/sec u
3. tan u = 1/cot u
4. csc u = 1/sin u
5. sec u = 1/cos u
6. cot u = 1/tan u

Front 2

Quotient Identities

Back 2

1. tan u = (sin u)/(cos u)
2. cot u = (cos u)/(sin u)

Front 3

Pythagorean Identities

Back 3

1. sin2 u + cos2 u = 1
2. 1 + tan2 u = sec2 u
3. 1 + cot2 u = csc2 u

Front 4

Even/Odd Identities

Back 4

1. sin (-u) = -sin u
2. cos (-u) = cos u
3. tan (-u) = -tan u
4. csc (-u) = -csc u
5. sec (-u) = sec u
6. cot (-u) = -cot u

Front 5

How should the even/odd identities be used?

Back 5

if an angle is negative, use those identities to make it positive

Front 6

What is the general format for cofunction identities?

Back 6

sin (pi/2 - u) = cos u

Front 7

Which trig functions go together for the cofunction identites?

Back 7

1. sin-cos
2. cos-sin
3. tan-cot
4. cot-tan
5. sec-csc
6. csc-sec

Front 8

When should the quotient identities be used?

Back 8

to replace tan or cot

Front 9

How do you derive the other two pythagorean identities from the first one (sin2 u + cos2 u = 1)?

Back 9

1. divide b cos2 u
2. divide by sin2 u