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Popular >

5cos(2x+3)=sin(2x+3)

Solución

5 cos (2 x + 3) = sin (2 x + 3)

Solución

x = \frac{1.37340 \dots}{2} + \frac{πn}{2} - \frac{3}{2}

+1

Grados

x = - 46.59863 \dots^{\circ} + 9 0^{\circ} n

Pasos de solución

5 cos (2 x + 3) = sin (2 x + 3)

Re-escribir usando identidades trigonométricas

5 cos (2 x + 3) = sin (2 x + 3)

Dividir ambos lados entre

cos (2 x + 3), cos (2 x + 3) \neq = 0

\frac{5 cos ( 2 x + 3 )}{cos ( 2 x + 3 )} = \frac{sin ( 2 x + 3 )}{cos ( 2 x + 3 )}

Simplificar

5 = \frac{sin ( 2 x + 3 )}{cos ( 2 x + 3 )}

Utilizar la identidad trigonométrica básica:

\frac{sin ( x )}{cos ( x )} = tan (x)

5 = tan (2 x + 3)

Intercambiar lados

tan (2 x + 3) = 5

tan (2 x + 3) = 5

Aplicar propiedades trigonométricas inversas

tan (2 x + 3) = 5

Soluciones generales para

tan (2 x + 3) = 5

tan (x) = a \Rightarrow x = arctan (a) + πn

2 x + 3 = arctan (5) + πn

2 x + 3 = arctan (5) + πn

Resolver

2 x + 3 = arctan (5) + πn : x = \frac{arctan ( 5 )}{2} + \frac{πn}{2} - \frac{3}{2}

2 x + 3 = arctan (5) + πn

Mover

3

al lado derecho

2 x + 3 = arctan (5) + πn

Restar

3

de ambos lados

2 x + 3 - 3 = arctan (5) + πn - 3

Simplificar

2 x = arctan (5) + πn - 3

2 x = arctan (5) + πn - 3

Dividir ambos lados entre

2

2 x = arctan (5) + πn - 3

Dividir ambos lados entre

2

\frac{2 x}{2} = \frac{arctan ( 5 )}{2} + \frac{πn}{2} - \frac{3}{2}

Simplificar

x = \frac{arctan ( 5 )}{2} + \frac{πn}{2} - \frac{3}{2}

x = \frac{arctan ( 5 )}{2} + \frac{πn}{2} - \frac{3}{2}

x = \frac{arctan ( 5 )}{2} + \frac{πn}{2} - \frac{3}{2}

Mostrar soluciones en forma decimal

x = \frac{1.37340 \dots}{2} + \frac{πn}{2} - \frac{3}{2}

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\frac{sin ^{2} ( x )}{1 - cos ^{2} ( x )} = cot (x)

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