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4cos(x-45)+7=10

Solución

4 cos (x - 4 5^{\circ}) + 7 = 10

Solución

x = 0.72273 \dots + 36 0^{\circ} n + 4 5^{\circ}, x = 36 0^{\circ} - 0.72273 \dots + 36 0^{\circ} n + 4 5^{\circ}

+1

radianes

x = 0.72273 \dots + \frac{π}{4} + 2 πn, x = 2 π - 0.72273 \dots + \frac{π}{4} + 2 πn

Pasos de solución

4 cos (x - 4 5^{\circ}) + 7 = 10

Mover

7

al lado derecho

4 cos (x - 4 5^{\circ}) + 7 = 10

Restar

7

de ambos lados

4 cos (x - 4 5^{\circ}) + 7 - 7 = 10 - 7

Simplificar

4 cos (x - 4 5^{\circ}) = 3

4 cos (x - 4 5^{\circ}) = 3

Dividir ambos lados entre

4

4 cos (x - 4 5^{\circ}) = 3

Dividir ambos lados entre

4

\frac{4 cos ( x - 4 5 ^{\circ} )}{4} = \frac{3}{4}

Simplificar

cos (x - 4 5^{\circ}) = \frac{3}{4}

cos (x - 4 5^{\circ}) = \frac{3}{4}

Aplicar propiedades trigonométricas inversas

cos (x - 4 5^{\circ}) = \frac{3}{4}

Soluciones generales para

cos (x - 4 5^{\circ}) = \frac{3}{4}

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

x - 4 5^{\circ} = arccos (\frac{3}{4}) + 36 0^{\circ} n, x - 4 5^{\circ} = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n

x - 4 5^{\circ} = arccos (\frac{3}{4}) + 36 0^{\circ} n, x - 4 5^{\circ} = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n

Resolver

x - 4 5^{\circ} = arccos (\frac{3}{4}) + 36 0^{\circ} n : x = arccos (\frac{3}{4}) + 36 0^{\circ} n + 4 5^{\circ}

x - 4 5^{\circ} = arccos (\frac{3}{4}) + 36 0^{\circ} n

Mover

4 5^{\circ}

al lado derecho

x - 4 5^{\circ} = arccos (\frac{3}{4}) + 36 0^{\circ} n

Sumar

4 5^{\circ}

a ambos lados

x - 4 5^{\circ} + 4 5^{\circ} = arccos (\frac{3}{4}) + 36 0^{\circ} n + 4 5^{\circ}

Simplificar

x = arccos (\frac{3}{4}) + 36 0^{\circ} n + 4 5^{\circ}

x = arccos (\frac{3}{4}) + 36 0^{\circ} n + 4 5^{\circ}

Resolver

x - 4 5^{\circ} = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n : x = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n + 4 5^{\circ}

x - 4 5^{\circ} = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n

Mover

4 5^{\circ}

al lado derecho

x - 4 5^{\circ} = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n

Sumar

4 5^{\circ}

a ambos lados

x - 4 5^{\circ} + 4 5^{\circ} = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n + 4 5^{\circ}

Simplificar

x = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n + 4 5^{\circ}

x = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n + 4 5^{\circ}

x = arccos (\frac{3}{4}) + 36 0^{\circ} n + 4 5^{\circ}, x = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n + 4 5^{\circ}

Mostrar soluciones en forma decimal

x = 0.72273 \dots + 36 0^{\circ} n + 4 5^{\circ}, x = 36 0^{\circ} - 0.72273 \dots + 36 0^{\circ} n + 4 5^{\circ}

Ejemplos populares

cos^2(x)=3(1-sin(x))

cos^{2} (x) = 3 (1 - sin (x))

- 2 = 2 cos (3 θ)

cos (x) = \frac{4}{30}

solvefor t,x=sin(2t)+1 resolver para

t, x = sin (2 t) + 1

cos (x) = \frac{4}{35}