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885cos(θ)-70=cos(250)+250

Solução

885 cos (θ) - 70 = cos (25 0^{\circ}) + 25 0^{\circ}

θ = 1.48705 \dots + 36 0^{\circ} n, θ = 36 0^{\circ} - 1.48705 \dots + 36 0^{\circ} n

Radianos

θ = 1.48705 \dots + 2 πn, θ = 2 π - 1.48705 \dots + 2 πn

Passos da solução

885 cos (θ) - 70 = cos (25 0^{\circ}) + 25 0^{\circ}

Mova

70

para o lado direito

885 cos (θ) - 70 = cos (25 0^{\circ}) + 25 0^{\circ}

Adicionar

70

a ambos os lados

885 cos (θ) - 70 + 70 = cos (25 0^{\circ}) + 25 0^{\circ} + 70

Simplificar

885 cos (θ) = cos (25 0^{\circ}) + 25 0^{\circ} + 70

885 cos (θ) = cos (25 0^{\circ}) + 25 0^{\circ} + 70

Dividir ambos os lados por

885

885 cos (θ) = cos (25 0^{\circ}) + 25 0^{\circ} + 70

Dividir ambos os lados por

885

\frac{885 cos ( θ )}{885} = \frac{cos ( 25 0 ^{\circ} )}{885} + \frac{25 0 ^{\circ}}{885} + \frac{70}{885}

Simplificar

\frac{885 cos ( θ )}{885} = \frac{cos ( 25 0 ^{\circ} )}{885} + \frac{25 0 ^{\circ}}{885} + \frac{70}{885}

Simplificar

\frac{885 cos ( θ )}{885} : cos (θ)

\frac{885 cos ( θ )}{885}

Dividir:

\frac{885}{885} = 1

= cos (θ)

Simplificar

\frac{cos ( 25 0 ^{\circ} )}{885} + \frac{25 0 ^{\circ}}{885} + \frac{70}{885} : \frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{15930}

\frac{cos ( 25 0 ^{\circ} )}{885} + \frac{25 0 ^{\circ}}{885} + \frac{70}{885}

Aplicar a regra

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{cos ( 25 0 ^{\circ} ) + 25 0 ^{\circ} + 70}{885}

Simplificar

cos (25 0^{\circ}) + 25 0^{\circ} + 70

em uma fração:

\frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{18}

cos (25 0^{\circ}) + 25 0^{\circ} + 70

Converter para fração:

cos (25 0^{\circ}) = \frac{cos ( 25 0 ^{\circ} ) 18}{18}, 70 = \frac{70 \cdot 18}{18}

= \frac{cos ( 25 0 ^{\circ} ) \cdot 18}{18} + 25 0^{\circ} + \frac{70 \cdot 18}{18}

Já que os denominadores são iguais, combinar as frações:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{cos ( 25 0 ^{\circ} ) \cdot 18 + 450 0 ^{\circ} + 70 \cdot 18}{18}

Multiplicar os números:

70 \cdot 18 = 1260

= \frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{18}

= \frac{\frac{18 c o s ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{18}}{885}

Aplicar as propriedades das frações:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{cos ( 25 0 ^{\circ} ) \cdot 18 + 450 0 ^{\circ} + 1260}{18 \cdot 885}

Multiplicar os números:

18 \cdot 885 = 15930

= \frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{15930}

cos (θ) = \frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{15930}

cos (θ) = \frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{15930}

cos (θ) = \frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{15930}

Aplique as propriedades trigonométricas inversas

cos (θ) = \frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{15930}

Soluções gerais para

cos (θ) = \frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{15930}

cos (x) = a \Rightarrow x = arccos (a) + 36 0^{\circ} n, x = 36 0^{\circ} - arccos (a) + 36 0^{\circ} n

θ = arccos (\frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{15930}) + 36 0^{\circ} n, θ = 36 0^{\circ} - arccos (\frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{15930}) + 36 0^{\circ} n

θ = arccos (\frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{15930}) + 36 0^{\circ} n, θ = 36 0^{\circ} - arccos (\frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{15930}) + 36 0^{\circ} n

Mostrar soluções na forma decimal

θ = 1.48705 \dots + 36 0^{\circ} n, θ = 36 0^{\circ} - 1.48705 \dots + 36 0^{\circ} n

8 - 8 sin (x) = 5 cos^{2} (x)

0 = - \frac{9 π ^{2}}{3200} cos (\frac{π x}{80})

cos^{2} (a) + 2 sin (a) + 1 = 0

tan (x) = \frac{5}{15}

2 sin (x + \frac{π}{9}) = - 1