AP Calculus BC All Essential Trig

Standard Trig & Recipricals, Inverse Trig, and all REQUIRED Derivatives and Integrals to know before the test.

Pythagorean Identity with sin & cos

sin²(u) + cos²(u) = 1

Pythagorean Identity with tan & sec

1 + tan²(u) = sec²(u)

Pythagorean Identity with cot & csc

1 + cot²(u) = csc²(u)

Quotient Identity of sin(u)

1 / csc(u)

Quotient Identity of csc(u)

1 / sin(u)

Quotient Identity of cos(u)

1 / sec(u)

Quotient Identity of sec(u)

1 / cos(x)

Quotient Identity of cot(u)

1 / tan(u) = cos(u) / sin(u)

Quotient Identity of tan(u)

1 / cot(u) = sin(u) / cos(u)

tan(u) = ? (Basic Identity)

sin(u) / cos(u)

sin(-u) = ? (Even/Odd Identity)

-sin(u)

cos(-u) = ? (Even/Odd Identity)

cos(u)

tan(-u) = ? (Even/Odd Identity)

-tan(u)

d/dx[sin(u)] = ?

cos(u) × du

d/dx[cos(u)] = ?

-sin(u) × du

d/dx[tan(u)] = ?

sec²(u) × du

d/dx[cot(u)] = ?

-csc²(u) × du

d/dx[sec(u)]

sec(u) × tan(u) × du

d/dx[csc(u)] = ?

-csc(u) × cot(u) × du

d/dx[arcsin(u)] = ?

1 / [ √(1 - u²) ] × du

d/dx[arccos(u)] = ?

-1 / [ √(1 - u²) ] × du

d/dx[arctan(u)] = ?

= 1 / (1 + u²) × du

d/dx[arccot(u)] = ?

= -1 / (1 + u²) × du

d/dx[arcsec(u)] = ?

1 / [ |u| × √(u² - 1) ] × du

d/dx[arccsc(u)] = ?

-1 / [ |u| × √(u² - 1) ] × du

∫ [sin(u)du] = ?

-cos(u) + C

∫ [cos(u)du] = ?

sin(u) + C

∫ [sec²(u)du] = ?

tan(u) + C

∫ [csc²(u)du] = ?

-cot(u) + C

∫ [sec(u) × tan(u) × du] = ?

sec(u) + C

∫ [csc(u) × cot(u) × du] = ?

-csc(u) + C

∫ [ du / √(a² - u²) ] = ?

arcsin(u / a) + C

∫ [ du / (a² - u²) ] = ?

(1 / a) × arctan(u / a) + C

∫ [ du / (u × √(u² - a²) ] = ?

(1 / a) × arcsec( |u| / a ) + C

sin²(x) = ? (Power-Reduction)

[ 1 - cos(2x) ] / 2

cos²(x) = ? (Power-Reduction)

[ 1 + cos(2x) ] / 2