Trig Identities

Question 1

What is the derivative of sin(x)?

Answer 1

cos(x)

Question 2

What is the derivative of cos(x)?

Answer 2

-sin(x)

Question 3

What is the derivative of tan(x)?

Answer 3

sec^2(x)

Question 4

True or False: The integral of sin(x) is -cos(x) + C.

Answer 4

True

Question 5

Fill in the blank: The derivative of sec(x) is ____.

Answer 5

sec(x)tan(x)

Question 6

What is the integral of cos(x)?

Answer 6

sin(x) + C

Question 7

What is the derivative of csc(x)?

Answer 7

-csc(x)cot(x)

Question 8

What is the integral of sec(x)tan(x)?

Answer 8

sec(x) + C

Question 9

What is the derivative of cot(x)?

Answer 9

-csc^2(x)

Question 10

True or False: The integral of csc(x) is -ln|csc(x) + cot(x)| + C.

Answer 10

True

Question 11

What is the integral of tan(x)?

Answer 11

-ln|cos(x)| + C

Question 12

Fill in the blank: The derivative of cosh(x) is ____.

Answer 12

sinh(x)

Question 13

What is the derivative of sinh(x)?

Answer 13

cosh(x)

Question 14

What is the integral of sinh(x)?

Answer 14

cosh(x) + C

Question 15

What is the integral of cosh(x)?

Answer 15

sinh(x) + C

Question 16

Fill in the blank: The derivative of tanh(x) is ____.

Answer 16

sech^2(x)

Question 17

What is the integral of sech^2(x)?

Answer 17

tanh(x) + C

Question 18

What is the derivative of sec(x)?

Answer 18

sec(x)tan(x)

Question 19

True or False: The integral of cot(x) is ln|sin(x)| + C.

Answer 19

False

Question 20

What is the integral of csch(x)?

Answer 20

-ln|csch(x) + coth(x)| + C

Question 21

What is the derivative of csch(x)?

Answer 21

-csch(x)coth(x)

Question 22

Fill in the blank: The derivative of arcsin(x) is ____.

Answer 22

1/sqrt(1 - x^2)

Question 23

What is the integral of arcsin(x)?

Answer 23

x*arcsin(x) + sqrt(1 - x^2) + C

Question 24

True or False: The derivative of arccos(x) is -1/sqrt(1 - x^2).

Answer 24

True

Question 25

What is the integral of arctan(x)?

Answer 25

x*arctan(x) - (1/2)ln(1 + x^2) + C

Question 26

Fill in the blank: The derivative of arccot(x) is ____.

Answer 26

-1/(1 + x^2)

Question 27

What is the derivative of arcsec(x)?

Answer 27

1/(|x|sqrt(x^2 - 1))

Question 28

What is the integral of arcsinh(x)?

Answer 28

x*arcsinh(x) - sqrt(x^2 + 1) + C