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1sin(45)=2.42sin(r)

Solução

1 sin (4 5^{\circ}) = 2.42 sin (r)

r = 0.29651 \dots + 36 0^{\circ} n, r = 18 0^{\circ} - 0.29651 \dots + 36 0^{\circ} n

Radianos

r = 0.29651 \dots + 2 πn, r = π - 0.29651 \dots + 2 πn

Passos da solução

1 \cdot sin (4 5^{\circ}) = 2.42 sin (r)

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\circ})

Utilizar a seguinte identidade trivial:

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\circ})

sin (x)

tabela de periodicidade com ciclo de

36 0^{\circ} n

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}

= \frac{2}{2}

= \frac{2}{2}

1 \cdot \frac{2}{2} = 2.42 sin (r)

Trocar lados

2.42 sin (r) = 1 \cdot \frac{2}{2}

Multiplicar ambos os lados por

100

2.42 sin (r) = 1 \cdot \frac{2}{2}

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

2.42 sin (r) \cdot 100 = 1 \cdot \frac{2}{2} \cdot 100

Simplificar

242 sin (r) = 502

242 sin (r) = 502

Dividir ambos os lados por

242

242 sin (r) = 502

Dividir ambos os lados por

242

\frac{242 sin ( r )}{242} = \frac{50 2}{242}

Simplificar

sin (r) = \frac{25 2}{121}

sin (r) = \frac{25 2}{121}

Aplique as propriedades trigonométricas inversas

sin (r) = \frac{25 2}{121}

Soluções gerais para

sin (r) = \frac{25 2}{121}

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

r = arcsin (\frac{25 2}{121}) + 36 0^{\circ} n, r = 18 0^{\circ} - arcsin (\frac{25 2}{121}) + 36 0^{\circ} n

r = arcsin (\frac{25 2}{121}) + 36 0^{\circ} n, r = 18 0^{\circ} - arcsin (\frac{25 2}{121}) + 36 0^{\circ} n

Mostrar soluções na forma decimal

r = 0.29651 \dots + 36 0^{\circ} n, r = 18 0^{\circ} - 0.29651 \dots + 36 0^{\circ} n

sec (x) = 4 sin (x)

sinh (nπ) = 0

x, z = sin (x y^{2})

3 sin^{2} (θ) + 2 cos (2 θ) = 1

sin^{4} (x) = 1