English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Trigonometria >

0=cos(20t)-cos(20.02t)

Solução

0 = cos (20 t) - cos (20.02 t)

Solução

t = 200 πn, t = 100 π + 200 πn, t = \frac{200 πn}{2001}, t = \frac{100 π}{2001} + \frac{200 πn}{2001}

Graus

t = 0^{\circ} + 3600 0^{\circ} n, t = 1800 0^{\circ} + 3600 0^{\circ} n, t = 0^{\circ} + 17.99100 \dots^{\circ} n, t = 8.99550 \dots^{\circ} + 17.99100 \dots^{\circ} n

Passos da solução

0 = cos (20 t) - cos (20.02 t)

Trocar lados

cos (20 t) - cos (20.02 t) = 0

Reeecreva usando identidades trigonométricas

- cos (20.02 t) + cos (20 t)

Use a identidade da transformação de soma em produto:

cos (s) - cos (t) = - 2 sin (\frac{s + t}{2}) sin (\frac{s - t}{2})

= - 2 sin (\frac{20 t + 20.02 t}{2}) sin (\frac{20 t - 20.02 t}{2})

Simplificar

- 2 sin (\frac{20 t + 20.02 t}{2}) sin (\frac{20 t - 20.02 t}{2}) : 2 sin (0.01 t) sin (20.01 t)

- 2 sin (\frac{20 t + 20.02 t}{2}) sin (\frac{20 t - 20.02 t}{2})

Somar elementos similares:

20 t + 20.02 t = 40.02 t

= - 2 sin (\frac{40.02 t}{2}) sin (\frac{20 t - 20.02 t}{2})

\frac{20 t - 20.02 t}{2} = - \frac{0.02 t}{2}

\frac{20 t - 20.02 t}{2}

Somar elementos similares:

20 t - 20.02 t = - 0.02 t

= \frac{- 0.02 t}{2}

Aplicar as propriedades das frações:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{0.02 t}{2}

= - 2 sin (\frac{40.02 t}{2}) sin (- \frac{0.02 t}{2})

Use a identidade de ângulo negativo:

sin (- x) = - sin (x)

= - 2 (- sin (\frac{0.02 t}{2})) sin (\frac{40.02 t}{2})

Aplicar a regra

- (- a) = a

= 2 sin (\frac{0.02 t}{2}) sin (\frac{40.02 t}{2})

Dividir:

\frac{0.02}{2} = 0.01

= 2 sin (0.01 t) sin (\frac{40.02 t}{2})

Dividir:

\frac{40.02}{2} = 20.01

= 2 sin (0.01 t) sin (20.01 t)

= 2 sin (0.01 t) sin (20.01 t)

2 sin (0.01 t) sin (20.01 t) = 0

Resolver cada parte separadamente

sin (0.01 t) = 0 or sin (20.01 t) = 0

sin (0.01 t) = 0 : t = 200 πn, t = 100 π + 200 πn

sin (0.01 t) = 0

Soluções gerais para

sin (0.01 t) = 0

sin (x)

tabela de periodicidade com ciclo de

2 πn

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

0.01 t = 0 + 2 πn, 0.01 t = π + 2 πn

0.01 t = 0 + 2 πn, 0.01 t = π + 2 πn

Resolver

0.01 t = 0 + 2 πn : t = 200 πn

0.01 t = 0 + 2 πn

0 + 2 πn = 2 πn

0.01 t = 2 πn

Multiplicar ambos os lados por

100

0.01 t = 2 πn

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

2

digits to the right of the decimal point, therefore multiply by

100

0.01 t \cdot 100 = 2 πn \cdot 100

Simplificar

t = 200 πn

t = 200 πn

Resolver

0.01 t = π + 2 πn : t = 100 π + 200 πn

0.01 t = π + 2 πn

Multiplicar ambos os lados por

100

0.01 t = π + 2 πn

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

2

digits to the right of the decimal point, therefore multiply by

100

0.01 t \cdot 100 = π 100 + 2 πn \cdot 100

Simplificar

t = 100 π + 200 πn

t = 100 π + 200 πn

t = 200 πn, t = 100 π + 200 πn

sin (20.01 t) = 0 : t = \frac{200 πn}{2001}, t = \frac{100 π}{2001} + \frac{200 πn}{2001}

sin (20.01 t) = 0

Soluções gerais para

sin (20.01 t) = 0

sin (x)

tabela de periodicidade com ciclo de

2 πn

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

20.01 t = 0 + 2 πn, 20.01 t = π + 2 πn

20.01 t = 0 + 2 πn, 20.01 t = π + 2 πn

Resolver

20.01 t = 0 + 2 πn : t = \frac{200 πn}{2001}

20.01 t = 0 + 2 πn

0 + 2 πn = 2 πn

20.01 t = 2 πn

Multiplicar ambos os lados por

100

20.01 t = 2 πn

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

2

digits to the right of the decimal point, therefore multiply by

100

20.01 t \cdot 100 = 2 πn \cdot 100

Simplificar

2001 t = 200 πn

2001 t = 200 πn

Dividir ambos os lados por

2001

2001 t = 200 πn

Dividir ambos os lados por

2001

\frac{2001 t}{2001} = \frac{200 πn}{2001}

Simplificar

t = \frac{200 πn}{2001}

t = \frac{200 πn}{2001}

Resolver

20.01 t = π + 2 πn : t = \frac{100 π}{2001} + \frac{200 πn}{2001}

20.01 t = π + 2 πn

Multiplicar ambos os lados por

100

20.01 t = π + 2 πn

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

2

digits to the right of the decimal point, therefore multiply by

100

20.01 t \cdot 100 = π 100 + 2 πn \cdot 100

Simplificar

2001 t = 100 π + 200 πn

2001 t = 100 π + 200 πn

Dividir ambos os lados por

2001

2001 t = 100 π + 200 πn

Dividir ambos os lados por

2001

\frac{2001 t}{2001} = \frac{100 π}{2001} + \frac{200 πn}{2001}

Simplificar

t = \frac{100 π}{2001} + \frac{200 πn}{2001}

t = \frac{100 π}{2001} + \frac{200 πn}{2001}

t = \frac{200 πn}{2001}, t = \frac{100 π}{2001} + \frac{200 πn}{2001}

Combinar toda as soluções

t = 200 πn, t = 100 π + 200 πn, t = \frac{200 πn}{2001}, t = \frac{100 π}{2001} + \frac{200 πn}{2001}

Gráfico

Exemplos populares

2tan(2x-10)=3.4641

2 tan (2 x - 10) = 3.4641

12cos(pi/3 x)+8=0

12 cos (\frac{π}{3} x) + 8 = 0

(sin(45))/(497.01)=(sin(x))/(450)

\frac{sin ( 4 5 ^{\circ} )}{497.01} = \frac{sin ( x )}{450}

(35)/(sin(A))=(60)/(sin(25))

\frac{35}{sin ( A )} = \frac{60}{sin ( 2 5 ^{\circ} )}

4csc(x)+sin(x)+5=0

4 csc (x) + sin (x) + 5 = 0