AP Calc Trig IDs

Question 1

D/dx [cos u]

Answer 1

-u’sin u

Question 2

D/dx [tan u]

Answer 2

u’sec^2 u

Question 3

D/dx [cot u]

Answer 3

-u’csc^2 u

Question 4

D/dx [sec u]

Answer 4

u’sec u tan u

Question 5

D/dx [csc u]

Answer 5

-u’csc u cot u

Question 6

D/dx [arcsin u]

Answer 6

u’/(1-u^2)^(1/2)

Question 7

D/dx [arccos u]

Answer 7

-u’/(1-u^2)^(1/2)

Question 8

D/dx [arctan u]

Answer 8

u’/(1+u^2)

Question 9

D/dx [arccot u]

Answer 9

-u’/(1+u^2)

Question 10

D/dx [sin u]

Answer 10

u’cos u

Question 11

D/dx [arcsec u]

Answer 11

u’/[|u|(u^2-1)^(1/2)]

Question 12

D/dx [arccsc u]

Answer 12

-u’/[|u|(u^2-1)^(1/2)]

Question 13

.{sin u du

Answer 13

-cos u + C

Question 14

{cos u du

Answer 14

sin u + C

Question 15

{tan u du

Answer 15

-ln|cos u| + C

Question 16

{cot u du

Answer 16

ln|sin u| + C

Question 17

{sec u du

Answer 17

ln|sec u + tan u| + C

Question 18

{csc u du

Answer 18

-ln|csc u + cot u| + C

Question 19

{sec^2 u du

Answer 19

tan u + C

Question 20

{csc^2 u du

Answer 20

-cot u + C

Question 21

{sec u tan u du

Answer 21

sec u + C

Question 22

{csc u cot u du

Answer 22

-csc u + c

Question 23

{du/(a^2-u^2)^(1/2)

Answer 23

arcsin (u/a) + C

Question 24

{du/(a^2 + u^2)

Answer 24

(1/a)arctan(u/a) + C

Question 25

{du/[u(u^2 - a^2)^(1/2)]

Answer 25

(1/a)arcsec (|u|/a) + C

Question 26

sin 2u

Answer 26

2sin u cos u

Question 27

cos 2u

Answer 27

cos^2 u - sin^2 u =
2cos^2 u - 1 =
1 - 2sin^2 u

Question 28

tan 2u

Answer 28

(2tan u)/(1 - tan^2 u)

Question 29

sin^2 u

Answer 29

(1 - cos 2u)/2

Question 30

cos^2 u

Answer 30

(1 + cos 2u)/2

Question 31

tan^2 u

Answer 31

(1 - cos 2u)/(1 + cos 2u)

Question 32

sin^2 x + cos^2 x=

Answer 32

1

Question 33

1 + tan^2 x=

Answer 33

sec^2 x

Question 34

1 + cot^2 x=

Answer 34

csc^2 x