Trigonometric Functions Flashcards
Secant = sec x
1
———
cos x
Cosecant = cosec x
1
———
sin x
Cotangent = cot x
1 cos x
——— = ———
tan x sin x
sec^2 x
1 + tan^2 x
cosec^2 x
1 + cot^2 x
sin(A+B)
sinAcosB + cosAsinB
sin(A-B)
sinAcosB - cosAsinB
cos(A+B)
cosAcosB - sinAsinB
cos(A-B)
cosAcosB + sinAsinB
tan(A+B)
tanA + tanB
——————
1 - tanAtanB
tan(A-B)
tanA - tanB
——————
1 + tanAtanB
Differentiate y = sin kx
dy .
— = k cos kx
dx .
Differentiate y = cos kx
dy .
— = - k sin kx
dx .
Differentiate y = tan kx
dy
— = k sec^2 kx
dx
Differentiate y = e^kx
dy .
— = k e^kx
dx .
Differentiate y = ln (kx^n)
dy 1 d(kx^n)
— = ——— x ————
dx kx^n dx
Differentiate y = ln (kx)
dy d 1
— = —— (ln k + ln x) = —
dx dx x
Differentiate y = a^kx
dy d(kx)
— = —— x a^kx ln(a)
dx dx
Chain Rule y (f(x))
dy dy du
— = — x — Outside times inside
dx du dx
Product Rule y = uv
dy dv du
— = u — + v —
dx dx dx
. u
Quotient Rule y = —
v
. du dv
v — - u —
dy dx dx
— = ——————————
dx v^2differentiate y = cosec kx
dy d(kx)
— = —— x - cosec (kx) cot (kx)
dx dx
Differentiate y = sec kx
dy d(kx)
— = —— x sec (kx) tan (kx)
dx dx
Differentiate y = cot kx
dy d(kx)
— = —— x - cosec^2 (kx)
dx dx
Differentiate y = arcsin x
dy 1
— = ——————
dx (1- x^2)^1/2
Differentiate y = arccos x
dy - 1
— = ——————
dx (1- x^2)^1/2
Differentiate y = arctan x
dy 1
— = ————
dx 1+ x^2
cos^2 x
1+cos2x
————
2
sin^2 x
1 - cos2x
————
2
Differentiate u(x)^n
u = trig angle
n * u(x)^(n-1) * u’(x)
