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4.72^2=3.3^2+3.3^2-2(3.3)(3.3)cos(x)

Solución

4.7 2^{2} = 3. 3^{2} + 3. 3^{2} - 2 (3.3) (3.3) cos (x)

x = 1.59368 \dots + 2 πn, x = - 1.59368 \dots + 2 πn

Grados

x = 91.31123 \dots^{\circ} + 36 0^{\circ} n, x = - 91.31123 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

4.7 2^{2} = 3. 3^{2} + 3. 3^{2} - 2 (3.3) (3.3) cos (x)

Intercambiar lados

3. 3^{2} + 3. 3^{2} - 2 \cdot 3.3 \cdot 3.3 cos (x) = 4.7 2^{2}

Simplificar

3. 3^{2} + 3. 3^{2} - 2 \cdot 3.3 \cdot 3.3 cos (x) : 21.78 - 21.78 cos (x)

3. 3^{2} + 3. 3^{2} - 2 \cdot 3.3 \cdot 3.3 cos (x)

Sumar elementos similares:

3. 3^{2} + 3. 3^{2} = 2 \cdot 3. 3^{2}

= 2 \cdot 3. 3^{2} - 2 \cdot 3.3 \cdot 3.3 cos (x)

Multiplicar los numeros:

2 \cdot 3.3 \cdot 3.3 = 21.78

= 2 \cdot 3. 3^{2} - 21.78 cos (x)

2 \cdot 3. 3^{2} = 21.78

2 \cdot 3. 3^{2}

3. 3^{2} = 10.89

= 2 \cdot 10.89

Multiplicar los numeros:

2 \cdot 10.89 = 21.78

= 21.78

= 21.78 - 21.78 cos (x)

Simplificar

4.7 2^{2} : 22.2784

4.7 2^{2}

4.7 2^{2} = 22.2784

= 22.2784

21.78 - 21.78 cos (x) = 22.2784

Mover

21.78

al lado derecho

21.78 - 21.78 cos (x) = 22.2784

Restar

21.78

de ambos lados

21.78 - 21.78 cos (x) - 21.78 = 22.2784 - 21.78

Simplificar

- 21.78 cos (x) = 0.4984

- 21.78 cos (x) = 0.4984

Dividir ambos lados entre

- 21.78

- 21.78 cos (x) = 0.4984

Dividir ambos lados entre

- 21.78

\frac{- 21.78 cos ( x )}{- 21.78} = \frac{0.4984}{- 21.78}

Simplificar

cos (x) = - \frac{0.4984}{21.78}

cos (x) = - \frac{0.4984}{21.78}

Aplicar propiedades trigonométricas inversas

cos (x) = - \frac{0.4984}{21.78}

Soluciones generales para

cos (x) = - \frac{0.4984}{21.78}

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

x = arccos (- \frac{0.4984}{21.78}) + 2 πn, x = - arccos (- \frac{0.4984}{21.78}) + 2 πn

x = arccos (- \frac{0.4984}{21.78}) + 2 πn, x = - arccos (- \frac{0.4984}{21.78}) + 2 πn

Mostrar soluciones en forma decimal

x = 1.59368 \dots + 2 πn, x = - 1.59368 \dots + 2 πn

2 sin (x - 3 0^{\circ}) = cos (x - 6 0^{\circ})

1 = 2 cos (3 x)

sec (b) = \frac{1}{2}

2 cos (2 x) = sin (2 x)

0.322 = sin (3.92232 \cdot t)