Trig Identities Flashcards
What is the derivative of sin(x)?
cos(x)
What is the derivative of cos(x)?
-sin(x)
What is the derivative of tan(x)?
sec^2(x)
True or False: The integral of sin(x) is -cos(x) + C.
True
Fill in the blank: The derivative of sec(x) is ____.
sec(x)tan(x)
What is the integral of cos(x)?
sin(x) + C
What is the derivative of csc(x)?
-csc(x)cot(x)
What is the integral of sec(x)tan(x)?
sec(x) + C
What is the derivative of cot(x)?
-csc^2(x)
True or False: The integral of csc(x) is -ln|csc(x) + cot(x)| + C.
True
What is the integral of tan(x)?
-ln|cos(x)| + C
Fill in the blank: The derivative of cosh(x) is ____.
sinh(x)
What is the derivative of sinh(x)?
cosh(x)
What is the integral of sinh(x)?
cosh(x) + C
What is the integral of cosh(x)?
sinh(x) + C
Fill in the blank: The derivative of tanh(x) is ____.
sech^2(x)
What is the integral of sech^2(x)?
tanh(x) + C
What is the derivative of sec(x)?
sec(x)tan(x)
True or False: The integral of cot(x) is ln|sin(x)| + C.
False
What is the integral of csch(x)?
-ln|csch(x) + coth(x)| + C
What is the derivative of csch(x)?
-csch(x)coth(x)
Fill in the blank: The derivative of arcsin(x) is ____.
1/sqrt(1 - x^2)
What is the integral of arcsin(x)?
x*arcsin(x) + sqrt(1 - x^2) + C
True or False: The derivative of arccos(x) is -1/sqrt(1 - x^2).
True
What is the integral of arctan(x)?
x*arctan(x) - (1/2)ln(1 + x^2) + C
Fill in the blank: The derivative of arccot(x) is ____.
-1/(1 + x^2)
What is the derivative of arcsec(x)?
1/(|x|sqrt(x^2 - 1))
What is the integral of arcsinh(x)?
x*arcsinh(x) - sqrt(x^2 + 1) + C
