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cos(θ)=(202)/(sqrt(331)*2\sqrt{33)}

Solução

cos (θ) = \frac{202}{331 \cdot 2 33}

θ = 0.26001 \dots + 2 πn, θ = 2 π - 0.26001 \dots + 2 πn

Radianos

θ = 0.26001 \dots + 6.28318 \dots n, θ = 6.02316 \dots + 6.28318 \dots n

Passos da solução

cos (θ) = \frac{202}{331 \cdot 2 33}

Simplificar

\frac{202}{331 \cdot 2 33} : \frac{101 10923}{10923}

\frac{202}{331 \cdot 2 33}

Dividir:

\frac{202}{2} = 101

= \frac{101}{331 33}

Simplificar

33133 : 10923

33133

Aplicar as propriedades dos radicais:

a b = a \cdot b

33133 = 331 \cdot 33

= 331 \cdot 33

Multiplicar os números:

331 \cdot 33 = 10923

= 10923

= \frac{101}{10923}

Racionalizar

\frac{101}{10923} : \frac{101 10923}{10923}

\frac{101}{10923}

Multiplicar pelo conjugado

\frac{10923}{10923}

= \frac{101 10923}{10923 10923}

1092310923 = 10923

1092310923

Aplicar as propriedades dos radicais:

a a = a

1092310923 = 10923

= 10923

= \frac{101 10923}{10923}

= \frac{101 10923}{10923}

cos (θ) = \frac{101 10923}{10923}

Aplique as propriedades trigonométricas inversas

cos (θ) = \frac{101 10923}{10923}

Soluções gerais para

cos (θ) = \frac{101 10923}{10923}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

θ = arccos (\frac{101 10923}{10923}) + 2 πn, θ = 2 π - arccos (\frac{101 10923}{10923}) + 2 πn

θ = arccos (\frac{101 10923}{10923}) + 2 πn, θ = 2 π - arccos (\frac{101 10923}{10923}) + 2 πn

Mostrar soluções na forma decimal

θ = 0.26001 \dots + 2 πn, θ = 2 π - 0.26001 \dots + 2 πn

5 sin (θ) + 12 cos (θ) = 13

2 - 2 cos^{2} (x) + 3 cos (x) = 0

cot (x) = \frac{5}{12}, π < x < \frac{3 π}{2}

tan (x) = \frac{1}{5}, tan (x + \frac{π}{2})

2 cos (5 x) = 0