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2/pi arccos(m*1-1)=0

Solución

\frac{2}{π} arccos (m \cdot 1 - 1) = 0

Solución

m = 2

Pasos de solución

\frac{2}{π} arccos (m \cdot 1 - 1) = 0

Multiplicar ambos lados por

π

\frac{2}{π} arccos (m 1 - 1) = 0

Multiplicar ambos lados por

π

\frac{2}{π} arccos (m 1 - 1) π = 0 π

Simplificar

2 arccos (m 1 - 1) = 0

2 arccos (m 1 - 1) = 0

Dividir ambos lados entre

2

2 arccos (m 1 - 1) = 0

Dividir ambos lados entre

2

\frac{2 arccos ( m 1 - 1 )}{2} = \frac{0}{2}

Simplificar

arccos (m 1 - 1) = 0

arccos (m 1 - 1) = 0

Aplicar propiedades trigonométricas inversas

arccos (m \cdot 1 - 1) = 0

arccos (x) = a \Rightarrow x = cos (a)

m \cdot 1 - 1 = cos (0)

cos (0) = 1

cos (0)

Utilizar la siguiente identidad trivial:

cos (0) = 1

cos (0)

cos (x)

tabla de valores periódicos con

2 πn

intervalos:

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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 1

= 1

m \cdot 1 - 1 = 1

m \cdot 1 - 1 = 1

Resolver

m \cdot 1 - 1 = 1 : m = 2

m \cdot 1 - 1 = 1

Multiplicar:

m \cdot 1 = m

m - 1 = 1

Mover

1

al lado derecho

m - 1 = 1

Sumar

1

a ambos lados

m - 1 + 1 = 1 + 1

Simplificar

m = 2

m = 2

m = 2

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