AP Calculus BC Study Guide with complete solutions

AP Calculus BC Study Guide

sin² θ + cos² θ = - Correct Answers -1

1 + tan² θ = - Correct Answers -sec² θ

1 + cot² θ = - Correct Answers -csc² θ

sin(-θ) = - Correct Answers --sin θ

cos(-θ) = - Correct Answers -cos θ

tan(-θ) = - Correct Answers --tan θ

sin(A + B) = - Correct Answers -sinAcosB + sinBcosA

sin(A - B) = - Correct Answers -sinAcosB - sinBcosA

cos(A + B) = - Correct Answers -cosAcosB - sinAsinB

cos(A - B) = - Correct Answers -cosAcosB + sinAsinB

sin 2θ = - Correct Answers -2sinθcosθ

cos 2θ = - Correct Answers -cos² θ - sin² θ
= 2cos² θ - 1
= 1 - 2sin² θ

tan θ = - Correct Answers -sin θ / cos θ
= 1 / cot θ

cot θ = - Correct Answers -cos θ / sin θ
= 1 / tan θ

sec θ = - Correct Answers -1 / cos θ

csc θ = - Correct Answers -1 / sin θ

cos² θ = - Correct Answers -()(1 + cos 2θ)

sin² θ = - Correct Answers -()(1 - cos 2θ)

, d/dx (x^n) = - Correct Answers -nx^(n - 1)

d/dx (fg) = - Correct Answers -fg' + gf'

d/dx (f / g) = - Correct Answers -(gf' - fg') / g^2

d/dx f(g(x)) = - Correct Answers -f'(g(x))g'(x)

d/dx (sin x) = - Correct Answers -cos x

d/dx (cos x) = - Correct Answers --sin x

d/dx (tan x) = - Correct Answers -sec² x

d/dx (cot x) = - Correct Answers --csc² x

d/dx (sec x) = - Correct Answers -secxtanx

d/dx (csc x) = - Correct Answers --cscxcotx

d/dx (e^x) = - Correct Answers -e^x

d/dx (a^x) = - Correct Answers -a^x * ln a

d/dx (ln x) = - Correct Answers -1 / x

d/dx (Arcsin x) = - Correct Answers -1 / √(1 - x²)

d/dx (Arctan x) = - Correct Answers -1 / (1 + x²)

d/dx (Arcsec x) = - Correct Answers -1 / (|x| * √(x² - 1))

d/dx (Arccos x) = - Correct Answers --1 / √(1 - x²)

d/dx (Arccot x) = - Correct Answers -1 / (1 + x²)

d/dx (Arccsc x) = - Correct Answers --1 / (|x| * √(x² - 1))

d/dx [c] = - Correct Answers -0

d/dx [cf(x)] = - Correct Answers -cf'(x)

∫a dx = - Correct Answers -ax + C

∫x^n dx = - Correct Answers -(x^n+1) / (n + 1) + C,
n≠1