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1.65^2=0.65^2+1.77^2-2(0.65)(1.77)cos(A)

Solución

1.6 5^{2} = 0.6 5^{2} + 1.7 7^{2} - 2 (0.65) (1.77) cos (A)

A = 1.20041 \dots + 2 πn, A = 2 π - 1.20041 \dots + 2 πn

Grados

A = 68.77858 \dots^{\circ} + 36 0^{\circ} n, A = 291.22141 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

1.6 5^{2} = 0.6 5^{2} + 1.7 7^{2} - 2 (0.65) (1.77) cos (A)

Intercambiar lados

0.6 5^{2} + 1.7 7^{2} - 2 \cdot 0.65 \cdot 1.77 cos (A) = 1.6 5^{2}

Multiplicar los numeros:

2 \cdot 0.65 \cdot 1.77 = 2.301

0.6 5^{2} + 1.7 7^{2} - 2.301 cos (A) = 1.6 5^{2}

0.6 5^{2} = 0.4225

0.4225 + 1.7 7^{2} - 2.301 cos (A) = 1.6 5^{2}

1.7 7^{2} = 3.1329

0.4225 + 3.1329 - 2.301 cos (A) = 1.6 5^{2}

Sumar:

0.4225 + 3.1329 = 3.5554

- 2.301 cos (A) + 3.5554 = 1.6 5^{2}

1.6 5^{2} = 2.7225

- 2.301 cos (A) + 3.5554 = 2.7225

Mover

3.5554

al lado derecho

- 2.301 cos (A) + 3.5554 = 2.7225

Restar

3.5554

de ambos lados

- 2.301 cos (A) + 3.5554 - 3.5554 = 2.7225 - 3.5554

Simplificar

- 2.301 cos (A) = - 0.8329

- 2.301 cos (A) = - 0.8329

Dividir ambos lados entre

- 2.301

- 2.301 cos (A) = - 0.8329

Dividir ambos lados entre

- 2.301

\frac{- 2.301 cos ( A )}{- 2.301} = \frac{- 0.8329}{- 2.301}

Simplificar

cos (A) = \frac{0.8329}{2.301}

cos (A) = \frac{0.8329}{2.301}

Aplicar propiedades trigonométricas inversas

cos (A) = \frac{0.8329}{2.301}

Soluciones generales para

cos (A) = \frac{0.8329}{2.301}

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

A = arccos (\frac{0.8329}{2.301}) + 2 πn, A = 2 π - arccos (\frac{0.8329}{2.301}) + 2 πn

A = arccos (\frac{0.8329}{2.301}) + 2 πn, A = 2 π - arccos (\frac{0.8329}{2.301}) + 2 πn

Mostrar soluciones en forma decimal

A = 1.20041 \dots + 2 πn, A = 2 π - 1.20041 \dots + 2 πn

x, cos (3 x + \frac{π}{4}) = \frac{1}{2}

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

x, cos^{2} (3 x + \frac{π}{4}) = \frac{3}{4}

\frac{tan ( x ^{2} + 6 ) - 1}{tan ( x )} = 0

tan (θ) = \frac{8}{- 8}