sin 2q = 2 cos q sin q
cos 2q = cos² q - sin² q = 2 cos² q - 1 = 1 - 2 sin² q
tan 2q = 2 tan q/ (1 - tan²q)

sin q/2 = ± Ö[(1 - cos q)/2]
cos q/2 = ± Ö[(1 + cos q)/2]
tan q/2 = sin q/(1 + cos q)

sin 3q = 3 sin q - 4 sin³ q
cos 3q = - 3 cos q + 4 cos³ q
tan 3q = (3 tan q - tan³ q)/ (1 - 3 tan²q)

cos² q + sin² q = 1
sec² q - tan² q = 1
cosec² q - cot² q = 1

sin² q = ½(1 - cos 2q)
cos² q = ½(1 + cos 2q)
tan² q = (1 - cos 2q) /(1 + cos 2q)

sin(A + B) = sin A cos B + cos A sin B
sin(A - B) = sin A cos B - cos A sin B
cos(A + B) = cos A cos B - sin A sin B
cos(A - B) = cos A cos B + sin A sin B
tan(A + B) = (tan A + tan B)/(1 - tan A tan B)
tan(A - B) = (tan A - tan B)/(1 + tan A tan B)

sin A + sin B = 2 sin ½(A + B) cos ½(A - B)
sin A - sin B = 2 cos ½(A + B) sin ½(A - B)
cos A + cos B = 2 cos ½(A + B) cos ½(A - B)
cos A - cos B = - 2 sin ½(A + B) sin ½(A - B)
tan A + tan B = sin (A + B)/(cos A cos B)
tan A - tan B = sin (A - B)/(cos A cos B)

sin²A + sin²B = 1 - cos(A + B)cos(A - B)
sin²A - sin²B = sin(A + B)sin(A - B)
cos²A + sin²B = 1 - sin(A + B)sin(A - B)
cos²A - sin²B = cos(A + B)cos(A - B)
cos²A + cos²B = 1 + cos(A + B)cos(A - B)
cos²A - cos²B = - sin(A + B)sin(A - B)

Afgeleiden:

d/dx (sin ax) = a cos ax
d/dx (cos ax) = -a sin ax
d/dx (tan ax) = a sec² ax

d/dx (1/sin x) = - cos x/sin² x
d/dx (1/cos x) = sin x/cos² x

d/dx (sin² ax) = a sin 2ax
d/dx (cos² ax) = - a sin 2ax

d/dx (sin^-1(x/a)) = 1/ Ö(a² - x²)
d/dx (cos^-1(x/a)) = - 1/ Ö(a² - x²)
d/dx (tan^-1(x/a)) = a/ (a² + x²)

Integralen:

ò (sin ax) dx = -(1/a) cos ax
ò (cos ax) dx = (1/a) sin ax
ò (tan ax) dx = -(1/a) log_e cos ax

ò (sin² ax) dx = x/2 - (1/4a) sin 2ax
ò (cos² ax) dx = x/2 + (1/4a) sin 2ax

ò (sinⁿ ax) dx = [(sin^{n - 1}ax cos ax)/na] + [(n - 1)/n] ò (sin^{n - 2} ax) dx
ò (cosⁿ ax) dx = [(cos^{n - 1}ax sin ax)/na] + [(n - 1)/n] ò (cos^{n - 2} ax) dx

ò (sin ax cos ax) dx = (1/2a) sin² ax
ò (sin m(ax) cos m(ax)) dx = (1/2a(m-n)) cos(m-n)ax - (1/2a(m+n)) cos(m+n)ax assuming m² ne n²
ò (sin² ax cos² ax) dx = (1/8)(x - (1/4a)sin 4ax)

ò (sin ax cos^m ax) dx = - (1/a(m+1)) cos^m+1 (ax)
ò (sin^m ax cos ax) dx = (1/a(m+1)) sin^m+1 (ax)

ò (x sin ax) dx = - (x/a) cos ax + a^-2 sin ax
ò (x cos ax) dx = (x/a) sin ax + a^-2 cos ax

ò (x² sin ax) dx = - (x² a^-1) cos ax + 2 x a^-2 sin ax + (2 a^-3) cos ax
ò (x² cos ax) dx = - (x² a^-1) sin ax - 2 x a^-2 cos ax + (2 a^-3) sin ax

Labo elektriciteit-elektronica