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4.3^2=3.8^2+6.3^2+2(3.8)(6.3)cos(b)

Solución

4. 3^{2} = 3. 8^{2} + 6. 3^{2} + 2 (3.8) (6.3) cos (b)

b = 2.41037 \dots + 2 πn, b = - 2.41037 \dots + 2 πn

Grados

b = 138.10423 \dots^{\circ} + 36 0^{\circ} n, b = - 138.10423 \dots^{\circ} + 36 0^{\circ} n

Pasos de solución

4. 3^{2} = 3. 8^{2} + 6. 3^{2} + 2 (3.8) (6.3) cos (b)

Intercambiar lados

3. 8^{2} + 6. 3^{2} + 2 \cdot 3.8 \cdot 6.3 cos (b) = 4. 3^{2}

Multiplicar los numeros:

2 \cdot 3.8 \cdot 6.3 = 47.88

3. 8^{2} + 6. 3^{2} + 47.88 cos (b) = 4. 3^{2}

3. 8^{2} = 14.44

14.44 + 6. 3^{2} + 47.88 cos (b) = 4. 3^{2}

6. 3^{2} = 39.69

14.44 + 39.69 + 47.88 cos (b) = 4. 3^{2}

Sumar:

14.44 + 39.69 = 54.13

47.88 cos (b) + 54.13 = 4. 3^{2}

4. 3^{2} = 18.49

47.88 cos (b) + 54.13 = 18.49

Multiplicar ambos lados por

100

47.88 cos (b) + 54.13 = 18.49

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

2

digits to the right of the decimal point, therefore multiply by

100

47.88 cos (b) \cdot 100 + 54.13 \cdot 100 = 18.49 \cdot 100

Simplificar

4788 cos (b) + 5413 = 1849

4788 cos (b) + 5413 = 1849

Mover

5413

al lado derecho

4788 cos (b) + 5413 = 1849

Restar

5413

de ambos lados

4788 cos (b) + 5413 - 5413 = 1849 - 5413

Simplificar

4788 cos (b) = - 3564

4788 cos (b) = - 3564

Dividir ambos lados entre

4788

4788 cos (b) = - 3564

Dividir ambos lados entre

4788

\frac{4788 cos ( b )}{4788} = \frac{- 3564}{4788}

Simplificar

\frac{4788 cos ( b )}{4788} = \frac{- 3564}{4788}

Simplificar

\frac{4788 cos ( b )}{4788} : cos (b)

\frac{4788 cos ( b )}{4788}

Dividir:

\frac{4788}{4788} = 1

= cos (b)

Simplificar

\frac{- 3564}{4788} : - \frac{99}{133}

\frac{- 3564}{4788}

Aplicar las propiedades de las fracciones:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{3564}{4788}

Eliminar los terminos comunes:

36

= - \frac{99}{133}

cos (b) = - \frac{99}{133}

cos (b) = - \frac{99}{133}

cos (b) = - \frac{99}{133}

Aplicar propiedades trigonométricas inversas

cos (b) = - \frac{99}{133}

Soluciones generales para

cos (b) = - \frac{99}{133}

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

b = arccos (- \frac{99}{133}) + 2 πn, b = - arccos (- \frac{99}{133}) + 2 πn

b = arccos (- \frac{99}{133}) + 2 πn, b = - arccos (- \frac{99}{133}) + 2 πn

Mostrar soluciones en forma decimal

b = 2.41037 \dots + 2 πn, b = - 2.41037 \dots + 2 πn

cos^{2} (x) - 4 cos (x) + 4 = 0

t, x - 4 = sec^{2} (t)

csc (θ) = \frac{34}{3}, cos (θ) > 0

2 sin^{2} (θ) - 3 sin (θ) cos (θ) + cos^{2} (θ) = 0

sin^{2} (x) + 4 cos^{2} (x) = 1