тригонометрия ◿

Определения:
  • a: a
  • b: b
  • c: c
  • h: h
  • alpha: угол α
  • beta: угол β
  • gamma: угол γ
  • x: x
  • y: y
  • z: z
Layer 1 a b c a b c Layer 1 C A B α

Теоремы Пифагора

\(c^2 = a^2 + b^2\)
\(c=sqrt(a^2+b^2)\)
c = c
a = a
b = b
\(a=sqrt( c^2-b^2 )\)
a = a
c = c
b = b
\(b=sqrt( c^2-a^2 )\)
b = b
c = c
a = a
\(c=sqrt(a^2+b^2)\)
c = c
a = a
b = b
\(a=sqrt( c^2-b^2 )\)
a = a
c = c
b = b
\(b=sqrt( c^2-a^2 )\)
b = b
c = c
a = a

a c Layer 1 C A B α

синус

\(x=sin(alpha)\)
x = x
alpha = угол α
\(alpha = asin(a/c)\)
alpha = угол α
a = a
c = c
\(a=sin(alpha)*c\)
a = a
alpha = угол α
c = c
\(h=a/sin(alpha)\)
h = h
a = a
alpha = угол α

b c Layer 1 C A B α

Kosinus

\(y=cos(alpha)\)
y = y
alpha = угол α
\(alpha = acos(b/h)\)
alpha = угол α
b = b
h = h
\(b=cos(alpha)*h\)
b = b
alpha = угол α
h = h
\(h=b/cos(alpha)\)
h = h
b = b
alpha = угол α

a b Layer 1 C A B α

касательный

\(z=tan(alpha)\)
z = z
alpha = угол α
\(alpha = atan(a/b)\)
alpha = угол α
a = a
b = b
\(a=tan(alpha)*b\)
a = a
alpha = угол α
b = b
\(b=a/tan(alpha)\)
b = b
a = a
alpha = угол α

a b c Layer 1 C A B α β γ

тригонометрические преобразования

\(alpha+beta+gamma=180\)
\(cos(alpha)^2+sin(alpha)^2=1\)
\(tan(alpha)=sin(alpha)/cos(alpha)\)
\(cot(alpha)=1/tan(alpha)\)
\(sin(alpha)=cos(90-alpha)\)
\(cos(alpha)=sin(90-alpha)\)
\(tan(alpha)=cot(90-alpha)\)
\(sin(2*alpha)=2*sin(alpha)*cos(alpha)\)
\(tan(2*alpha)=2*tan(alpha)/(1-tan(alpha)^2)\)
\(sin(3*alpha)=3*sin(alpha)-4*sin(alpha)^3\)
\(cos(alpha)^2=(1/2)+(1/2)*cos(2*alpha)\)