trigonometric identites

Question 1

reciprocal identities

Answer 1

1. cscθ = 1/sinθ
2. secθ = 1/cosθ
3. cotθ = 1/tanθ
4. tanθ=1/cotθ
5. cosθ=1/secθ
6. sinθ=1/cscθ

Question 2

quotient identities

Answer 2

1. tanθ = sinθ/cosθ
2. cotθ = cosθ/sinθ

Question 3

cosine difference formula

Answer 3

cos(A-B) = cosA cosB + sinA sinB

Question 4

Pythagorean identities

Answer 4

1. sin^2θ+cos^2θ = 1
2. 1 + tan^2θ = sec^2θ
3. 1 + cot^2θ = csc^2θ

Question 5

cosine sum formula

Answer 5

cos(A+B) = cosA cosB - sinA sinB

Question 6

sine sum formula

Answer 6

sin(A+B) = sinA cosB + cosA sinB

Question 7

sine difference formula

Answer 7

sin(A-B) = sinA cosB - cosA sinB

Question 8

tangent sum formula

Answer 8

tan(A+B)= tanA + tanB / 1 - tanA tanB

Question 9

tangent difference formula

Answer 9

tan(A-B) = tanA - tanB / 1 + tanA tanB

Question 10

sine double angle identity

Answer 10

sin(2x) = 2 sinx cosx

Question 11

cosine double angle identity

Answer 11

1. cos^2x - sin^2x
2. 2cos^2x - 1
3. 1- 2sin^2x

Question 12

tangent double angle identity

Answer 12

tan(2x) = 2 tanx / 1 - tan^2x

2 /1 small 2

Question 13

sine half angle identity

Answer 13

sin(1/2x) = √2-2cosx / 2

Question 14

cosine half angle identity

Answer 14

cos(1/2x) = √2cosx+2 / 2

cos half adds the other 2nd 1/2

Question 15

tangent half angle identity

Answer 15

1. tan(1/2x) = 1-cosx / sinx
2. tan(1/2x) = sinx / 1 + cosx

tan half has TWO different ones!
conjugate - top, conjugate + bottom

Question 16

law of cosine

Answer 16

a^2 = b^2 + c^2 + 2bc cosA
b^2 = a^2 + c^2 + 2ac cosB
c^2 = a^2 + b^2 + 2ab cosC
only use when SSS or SAS

Question 17

law of sine

Answer 17

sinA/a = sinB/b = sinC/c
only use when ASA

Question 18

product of z1z2

Answer 18

r1r2[cos(x1+x2) + isin(x1+x2)]

Question 19

quotient of z1z2

Answer 19

r1/r2[cos(x1-x2) + isin(x1-x2)]

Question 20

cofunction identities

Answer 20

1. cos(pi/2 - x) = sinx
2. sin(pi/2 - x) = cosx
3. cot(pi/2 - x) = tanx
4. tan(pi/2 - x) = cotx
5. csc(pi/2 - x) = secx
6. sec(pi/2 - x) = cscx