3B Trig Identities

Question 1

(quotient identities) tanx =

Answer 1

sinx/cosx

Question 2

(quotient identities) cotx =

Answer 2

cosx/sinx

Question 3

(even/odd identities) sin(-x) =

Answer 3

-sinx

Question 4

(even/odd identities) cos(-x) =

Answer 4

cosx

Question 5

(even/odd identities) tan(-x) =

Answer 5

-tanx

Question 6

(even/odd identities) csc(-x) =

Answer 6

-cscx

Question 7

(even/odd identities) sec(-x) =

Answer 7

secx

Question 8

(even/odd identities) cot(-x) =

Answer 8

-cotx

Question 9

sin^2 x + cos^2 x =

Answer 9

1

Question 10

1 + cot^2 x =

Answer 10

csc^2 x

Question 11

1 + tan^2 x =

Answer 11

sec^2 x

Question 12

sin(A + B) =

Answer 12

sinAcosB + cosAsinB

Question 13

cos(A + B) =

Answer 13

cosAcosB - sinAsinB

Question 14

tan(A + B) =

Answer 14

(tanA + tanB) / (1 - tanAtanB)

Question 15

sin(A - B) =

Answer 15

sinAcosB - cosAsinB

Question 16

cos(A - B) =

Answer 16

cosAcosB + sinAsinB

Question 17

tan(A - B) =

Answer 17

(tanA - tanB) / (1 + tanAtanB)

Question 18

sin(2x) =

Answer 18

2sinxcosx

Question 19

tan(2x) =

Answer 19

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

Question 20

cos(2x) =

Answer 20

cos^2 x - sin^2 x

or 1 - 2sin^2 x
or 2cos^2 x -1

Question 21

sin(x/2) =

Answer 21

+ or - sqrt( (1 - cosx) / 2)

Question 22

cos(x/2) =

Answer 22

+ or - sqrt( (1 + cosx) / 2)

Question 23

tan(x/2)

Answer 23

+ or - sqrt( (1 - cosx) / (1 + cosx))