Derivatives and Integrals of Trig Functions

(d/dx) sinx

cosx

d/dx(cosx)

-sinx

d/dx(secx)

sec(x)tan(x).

d/dx(cscx)

-csc(x)cot(x)

d/dx(tanx)

sec²(x).

d/dx(cotx)

-csc²(x)

d/dx(arcsinx)

1 / √(1 - x²).

d/dx(arccos)

-1 / √(1 - x²)

d/dx(arcsecx)

1/(|x| * √(x² - 1))

d/dx(arccscx)

-1 / (|x| * √(x^2 - 1)).

d/dx(arctanx)

1 / (1 + x^2)

d/dx(arccotx)

-1 / (1 + x^2)

∫(1/√(a²-u²))du

arcsin(u/a)+c

∫(-1/√(a²-u²))du

arccos(u/a) + c

∫(du/u√(u²-a²))

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

∫(-du/u√(u²-a²))

(1/a)arccsc(|u|/a)+c

∫(du/(a²+u²))

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

∫(-du/(a²+u²))

(1/a)arccot(u/a)+c

What is the range of arcsin?

[-π/2, π/2]

What is the domain of arcsin?

[-1, 1]

What is the domain of arccos?

[-1, 1]

What is the range of arccos?

[0, π]

What is the domain of arctan?

x∈ℝ

What is the range of arctan?

(-π/2, π/2)