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cos(W)=(170^2+173^2-125^2)/(2(170)(173))

Solución

cos (W) = \frac{17 0 ^{2} + 17 3 ^{2} - 12 5 ^{2}}{2 ( 170 ) ( 173 )}

W = 0.74584 \dots + 2 πn, W = 2 π - 0.74584 \dots + 2 πn

radianes

W = 0.74584 \dots + 6.28318 \dots n, W = 5.53733 \dots + 6.28318 \dots n

Pasos de solución

cos (W) = \frac{17 0 ^{2} + 17 3 ^{2} - 12 5 ^{2}}{2 ( 170 ) ( 173 )}

Simplificar

\frac{17 0 ^{2} + 17 3 ^{2} - 12 5 ^{2}}{2 \cdot 170 \cdot 173} : \frac{10801}{14705}

\frac{17 0 ^{2} + 17 3 ^{2} - 12 5 ^{2}}{2 \cdot 170 \cdot 173}

17 0^{2} + 17 3^{2} - 12 5^{2} = 43204

17 0^{2} + 17 3^{2} - 12 5^{2}

17 0^{2} = 28900

= 28900 + 17 3^{2} - 12 5^{2}

17 3^{2} = 29929

= 28900 + 29929 - 12 5^{2}

12 5^{2} = 15625

= 28900 + 29929 - 15625

Sumar/restar lo siguiente:

28900 + 29929 - 15625 = 43204

= 43204

= \frac{43204}{2 \cdot 170 \cdot 173}

Multiplicar los numeros:

2 \cdot 170 \cdot 173 = 58820

= \frac{43204}{58820}

Eliminar los terminos comunes:

4

= \frac{10801}{14705}

Aplicar propiedades trigonométricas inversas

cos (W) = \frac{10801}{14705}

Soluciones generales para

cos (W) = \frac{10801}{14705}

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

W = arccos (\frac{10801}{14705}) + 2 πn, W = 2 π - arccos (\frac{10801}{14705}) + 2 πn

W = arccos (\frac{10801}{14705}) + 2 πn, W = 2 π - arccos (\frac{10801}{14705}) + 2 πn

Mostrar soluciones en forma decimal

W = 0.74584 \dots + 2 πn, W = 2 π - 0.74584 \dots + 2 πn

2 csc^{2} (x) + csc (x) - 1 = 0

3 cos (θ) + sin (2 θ) = 0

sec (x) (sec (x) - 1) = 2

tan (x) = 0.15

cos (x) - sin (x) = 0, y (0) = 3