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sin(θ)=0.7cos(90-θ)

Solución

sin (θ) = 0.7 cos (9 0^{\circ} - θ)

Solución

θ = 36 0^{\circ} n, θ = 18 0^{\circ} + 36 0^{\circ} n

radianes

θ = 0 + 2 πn, θ = π + 2 πn

Pasos de solución

sin (θ) = 0.7 cos (9 0^{\circ} - θ)

Re-escribir usando identidades trigonométricas

sin (θ) = 0.7 cos (9 0^{\circ} - θ)

Re-escribir usando identidades trigonométricas

cos (9 0^{\circ} - θ)

Utilizar la identidad de diferencia de ángulos:

cos (s - t) = cos (s) cos (t) + sin (s) sin (t)

= cos (9 0^{\circ}) cos (θ) + sin (9 0^{\circ}) sin (θ)

Simplificar

cos (9 0^{\circ}) cos (θ) + sin (9 0^{\circ}) sin (θ) : sin (θ)

cos (9 0^{\circ}) cos (θ) + sin (9 0^{\circ}) sin (θ)

cos (9 0^{\circ}) cos (θ) = 0

cos (9 0^{\circ}) cos (θ)

Simplificar

cos (9 0^{\circ}) : 0

cos (9 0^{\circ})

Utilizar la siguiente identidad trivial:

cos (9 0^{\circ}) = 0

cos (x)

tabla de valores periódicos con

36 0^{\circ} n

intervalos:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 0

= 0 \cdot cos (θ)

Aplicar la regla

0 \cdot a = 0

= 0

sin (9 0^{\circ}) sin (θ) = sin (θ)

sin (9 0^{\circ}) sin (θ)

Simplificar

sin (9 0^{\circ}) : 1

sin (9 0^{\circ})

Utilizar la siguiente identidad trivial:

sin (9 0^{\circ}) = 1

tabla de valores periódicos con

36 0^{\circ} n

intervalos:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 1

= 1 \cdot sin (θ)

Multiplicar:

1 \cdot sin (θ) = sin (θ)

= sin (θ)

= 0 + sin (θ)

0 + sin (θ) = sin (θ)

= sin (θ)

= sin (θ)

sin (θ) = 0.7 sin (θ)

sin (θ) = 0.7 sin (θ)

Restar

0.7 sin (θ)

de ambos lados

0.3 sin (θ) = 0

Multiplicar ambos lados por

10

0.3 sin (θ) = 0

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere is one digit to the right of the decimal point, therefore multiply by

10

0.3 sin (θ) \cdot 10 = 0 \cdot 10

Simplificar

3 sin (θ) = 0

3 sin (θ) = 0

Dividir ambos lados entre

3

3 sin (θ) = 0

Dividir ambos lados entre

3

\frac{3 sin ( θ )}{3} = \frac{0}{3}

Simplificar

sin (θ) = 0

sin (θ) = 0

Soluciones generales para

sin (θ) = 0

tabla de valores periódicos con

36 0^{\circ} n

intervalos:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

θ = 0 + 36 0^{\circ} n, θ = 18 0^{\circ} + 36 0^{\circ} n

θ = 0 + 36 0^{\circ} n, θ = 18 0^{\circ} + 36 0^{\circ} n

Resolver

θ = 0 + 36 0^{\circ} n : θ = 36 0^{\circ} n

θ = 0 + 36 0^{\circ} n

0 + 36 0^{\circ} n = 36 0^{\circ} n

θ = 36 0^{\circ} n

θ = 36 0^{\circ} n, θ = 18 0^{\circ} + 36 0^{\circ} n

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cos (θ) = \frac{4}{2}

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