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3cos(4θ-26)+5=7,-30<= θ<45

Solución

3 cos (4 θ - 2 6^{\circ}) + 5 = 7, - 3 0^{\circ} \leq θ < 4 5^{\circ}

Solución

θ = \frac{234 0 ^{\circ} + 90 \cdot 0.84106 \dots}{360}, θ = \frac{234 0 ^{\circ} - 90 \cdot 0.84106 \dots}{360}

radianes

θ = \frac{13 π + 90 \cdot 0.84106 \dots}{360}, θ = \frac{13 π - 90 \cdot 0.84106 \dots}{360}

Pasos de solución

3 cos (4 θ - 2 6^{\circ}) + 5 = 7, - 3 0^{\circ} \leq θ < 4 5^{\circ}

Mover

5

al lado derecho

3 cos (4 θ - 2 6^{\circ}) + 5 = 7

Restar

5

de ambos lados

3 cos (4 θ - 2 6^{\circ}) + 5 - 5 = 7 - 5

Simplificar

3 cos (4 θ - 2 6^{\circ}) = 2

3 cos (4 θ - 2 6^{\circ}) = 2

Dividir ambos lados entre

3

3 cos (4 θ - 2 6^{\circ}) = 2

Dividir ambos lados entre

3

\frac{3 cos ( 4 θ - 2 6 ^{\circ} )}{3} = \frac{2}{3}

Simplificar

cos (4 θ - 2 6^{\circ}) = \frac{2}{3}

cos (4 θ - 2 6^{\circ}) = \frac{2}{3}

Aplicar propiedades trigonométricas inversas

cos (4 θ - 2 6^{\circ}) = \frac{2}{3}

Soluciones generales para

cos (4 θ - 2 6^{\circ}) = \frac{2}{3}

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

4 θ - 2 6^{\circ} = arccos (\frac{2}{3}) + 36 0^{\circ} n, 4 θ - 2 6^{\circ} = 36 0^{\circ} - arccos (\frac{2}{3}) + 36 0^{\circ} n

4 θ - 2 6^{\circ} = arccos (\frac{2}{3}) + 36 0^{\circ} n, 4 θ - 2 6^{\circ} = 36 0^{\circ} - arccos (\frac{2}{3}) + 36 0^{\circ} n

Resolver

4 θ - 2 6^{\circ} = arccos (\frac{2}{3}) + 36 0^{\circ} n : θ = \frac{18 0 ^{\circ} n}{2} + 6. 5^{\circ} + \frac{arccos ( \frac{2}{3} )}{4}

4 θ - 2 6^{\circ} = arccos (\frac{2}{3}) + 36 0^{\circ} n

Mover

2 6^{\circ}

al lado derecho

4 θ - 2 6^{\circ} = arccos (\frac{2}{3}) + 36 0^{\circ} n

Sumar

2 6^{\circ}

a ambos lados

4 θ - 2 6^{\circ} + 2 6^{\circ} = arccos (\frac{2}{3}) + 36 0^{\circ} n + 2 6^{\circ}

Simplificar

4 θ = arccos (\frac{2}{3}) + 36 0^{\circ} n + 2 6^{\circ}

4 θ = arccos (\frac{2}{3}) + 36 0^{\circ} n + 2 6^{\circ}

Dividir ambos lados entre

4

4 θ = arccos (\frac{2}{3}) + 36 0^{\circ} n + 2 6^{\circ}

Dividir ambos lados entre

4

\frac{4 θ}{4} = \frac{arccos ( \frac{2}{3} )}{4} + \frac{36 0 ^{\circ} n}{4} + \frac{2 6 ^{\circ}}{4}

Simplificar

\frac{4 θ}{4} = \frac{arccos ( \frac{2}{3} )}{4} + \frac{36 0 ^{\circ} n}{4} + \frac{2 6 ^{\circ}}{4}

Simplificar

\frac{4 θ}{4} : θ

\frac{4 θ}{4}

Dividir:

\frac{4}{4} = 1

= θ

Simplificar

\frac{arccos ( \frac{2}{3} )}{4} + \frac{36 0 ^{\circ} n}{4} + \frac{2 6 ^{\circ}}{4} : \frac{18 0 ^{\circ} n}{2} + 6. 5^{\circ} + \frac{arccos ( \frac{2}{3} )}{4}

\frac{arccos ( \frac{2}{3} )}{4} + \frac{36 0 ^{\circ} n}{4} + \frac{2 6 ^{\circ}}{4}

Agrupar términos semejantes

= \frac{36 0 ^{\circ} n}{4} + \frac{2 6 ^{\circ}}{4} + \frac{arccos ( \frac{2}{3} )}{4}

\frac{36 0 ^{\circ} n}{4} = \frac{18 0 ^{\circ} n}{2}

\frac{36 0 ^{\circ} n}{4}

Eliminar los terminos comunes:

2

= \frac{18 0 ^{\circ} n}{2}

\frac{2 6 ^{\circ}}{4} = 6. 5^{\circ}

\frac{2 6 ^{\circ}}{4}

Aplicar las propiedades de las fracciones:

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

= \frac{234 0 ^{\circ}}{90 \cdot 4}

Multiplicar los numeros:

90 \cdot 4 = 360

= 6. 5^{\circ}

= \frac{18 0 ^{\circ} n}{2} + 6. 5^{\circ} + \frac{arccos ( \frac{2}{3} )}{4}

θ = \frac{18 0 ^{\circ} n}{2} + 6. 5^{\circ} + \frac{arccos ( \frac{2}{3} )}{4}

θ = \frac{18 0 ^{\circ} n}{2} + 6. 5^{\circ} + \frac{arccos ( \frac{2}{3} )}{4}

θ = \frac{18 0 ^{\circ} n}{2} + 6. 5^{\circ} + \frac{arccos ( \frac{2}{3} )}{4}

Resolver

4 θ - 2 6^{\circ} = 36 0^{\circ} - arccos (\frac{2}{3}) + 36 0^{\circ} n : θ = 9 0^{\circ} + 6. 5^{\circ} + \frac{18 0 ^{\circ} n}{2} - \frac{arccos ( \frac{2}{3} )}{4}

4 θ - 2 6^{\circ} = 36 0^{\circ} - arccos (\frac{2}{3}) + 36 0^{\circ} n

Mover

2 6^{\circ}

al lado derecho

4 θ - 2 6^{\circ} = 36 0^{\circ} - arccos (\frac{2}{3}) + 36 0^{\circ} n

Sumar

2 6^{\circ}

a ambos lados

4 θ - 2 6^{\circ} + 2 6^{\circ} = 36 0^{\circ} - arccos (\frac{2}{3}) + 36 0^{\circ} n + 2 6^{\circ}

Simplificar

4 θ = 36 0^{\circ} - arccos (\frac{2}{3}) + 36 0^{\circ} n + 2 6^{\circ}

4 θ = 36 0^{\circ} - arccos (\frac{2}{3}) + 36 0^{\circ} n + 2 6^{\circ}

Dividir ambos lados entre

4

4 θ = 36 0^{\circ} - arccos (\frac{2}{3}) + 36 0^{\circ} n + 2 6^{\circ}

Dividir ambos lados entre

4

\frac{4 θ}{4} = 9 0^{\circ} - \frac{arccos ( \frac{2}{3} )}{4} + \frac{36 0 ^{\circ} n}{4} + \frac{2 6 ^{\circ}}{4}

Simplificar

\frac{4 θ}{4} = 9 0^{\circ} - \frac{arccos ( \frac{2}{3} )}{4} + \frac{36 0 ^{\circ} n}{4} + \frac{2 6 ^{\circ}}{4}

Simplificar

\frac{4 θ}{4} : θ

\frac{4 θ}{4}

Dividir:

\frac{4}{4} = 1

= θ

Simplificar

9 0^{\circ} - \frac{arccos ( \frac{2}{3} )}{4} + \frac{36 0 ^{\circ} n}{4} + \frac{2 6 ^{\circ}}{4} : 9 0^{\circ} + 6. 5^{\circ} + \frac{18 0 ^{\circ} n}{2} - \frac{arccos ( \frac{2}{3} )}{4}

9 0^{\circ} - \frac{arccos ( \frac{2}{3} )}{4} + \frac{36 0 ^{\circ} n}{4} + \frac{2 6 ^{\circ}}{4}

Agrupar términos semejantes

= 9 0^{\circ} + \frac{36 0 ^{\circ} n}{4} + \frac{2 6 ^{\circ}}{4} - \frac{arccos ( \frac{2}{3} )}{4}

9 0^{\circ} = 9 0^{\circ}

9 0^{\circ}

Eliminar los terminos comunes:

2

= 9 0^{\circ}

\frac{36 0 ^{\circ} n}{4} = \frac{18 0 ^{\circ} n}{2}

\frac{36 0 ^{\circ} n}{4}

Eliminar los terminos comunes:

2

= \frac{18 0 ^{\circ} n}{2}

\frac{2 6 ^{\circ}}{4} = 6. 5^{\circ}

\frac{2 6 ^{\circ}}{4}

Aplicar las propiedades de las fracciones:

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

= \frac{234 0 ^{\circ}}{90 \cdot 4}

Multiplicar los numeros:

90 \cdot 4 = 360

= 6. 5^{\circ}

= 9 0^{\circ} + \frac{18 0 ^{\circ} n}{2} + 6. 5^{\circ} - \frac{arccos ( \frac{2}{3} )}{4}

Agrupar términos semejantes

= 9 0^{\circ} + 6. 5^{\circ} + \frac{18 0 ^{\circ} n}{2} - \frac{arccos ( \frac{2}{3} )}{4}

θ = 9 0^{\circ} + 6. 5^{\circ} + \frac{18 0 ^{\circ} n}{2} - \frac{arccos ( \frac{2}{3} )}{4}

θ = 9 0^{\circ} + 6. 5^{\circ} + \frac{18 0 ^{\circ} n}{2} - \frac{arccos ( \frac{2}{3} )}{4}

θ = 9 0^{\circ} + 6. 5^{\circ} + \frac{18 0 ^{\circ} n}{2} - \frac{arccos ( \frac{2}{3} )}{4}

θ = \frac{18 0 ^{\circ} n}{2} + 6. 5^{\circ} + \frac{arccos ( \frac{2}{3} )}{4}, θ = 9 0^{\circ} + 6. 5^{\circ} + \frac{18 0 ^{\circ} n}{2} - \frac{arccos ( \frac{2}{3} )}{4}

Soluciones para el rango

- 3 0^{\circ} \leq θ < 4 5^{\circ}

θ = \frac{234 0 ^{\circ} + 90 arccos ( \frac{2}{3} )}{360}, θ = \frac{234 0 ^{\circ} - 90 arccos ( \frac{2}{3} )}{360}

Mostrar soluciones en forma decimal

θ = \frac{234 0 ^{\circ} + 90 \cdot 0.84106 \dots}{360}, θ = \frac{234 0 ^{\circ} - 90 \cdot 0.84106 \dots}{360}

Ejemplos populares

tan^2(θ)-tan(θ)=6,0<= θ<180

tan^{2} (θ) - tan (θ) = 6, 0^{\circ} \leq θ < 18 0^{\circ}

sin(x)=(2sqrt(3))/3

sin (x) = \frac{2 3}{3}

(sin(2x))/(cos(x))=0

\frac{sin ( 2 x )}{cos ( x )} = 0

12sin^2(x)=5cos(x)+9

12 sin^{2} (x) = 5 cos (x) + 9

cos(θ)=-(2sqrt(5))/5

cos (θ) = - \frac{2 5}{5}