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2sin(x)-cos(x)=0,0<= x<= 360

Solución

2 sin (x) - cos (x) = 0, 0^{\circ} \leq x \leq 36 0^{\circ}

x = 0.46364 \dots, x = 0.46364 \dots + 18 0^{\circ}

radianes

x = 0.46364 \dots, x = 0.46364 \dots + π

Pasos de solución

2 sin (x) - cos (x) = 0, 0^{\circ} \leq x \leq 36 0^{\circ}

Re-escribir usando identidades trigonométricas

2 sin (x) - cos (x) = 0

Dividir ambos lados entre

cos (x), cos (x) \neq = 0

\frac{2 sin ( x ) - cos ( x )}{cos ( x )} = \frac{0}{cos ( x )}

Simplificar

\frac{2 sin ( x )}{cos ( x )} - 1 = 0

Utilizar la identidad trigonométrica básica:

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

2 tan (x) - 1 = 0

2 tan (x) - 1 = 0

Mover

1

al lado derecho

2 tan (x) - 1 = 0

Sumar

1

a ambos lados

2 tan (x) - 1 + 1 = 0 + 1

Simplificar

2 tan (x) = 1

2 tan (x) = 1

Dividir ambos lados entre

2

2 tan (x) = 1

Dividir ambos lados entre

2

\frac{2 tan ( x )}{2} = \frac{1}{2}

Simplificar

tan (x) = \frac{1}{2}

tan (x) = \frac{1}{2}

Aplicar propiedades trigonométricas inversas

tan (x) = \frac{1}{2}

Soluciones generales para

tan (x) = \frac{1}{2}

tan (x) = a \Rightarrow x = arctan (a) + 18 0^{\circ} n

x = arctan (\frac{1}{2}) + 18 0^{\circ} n

x = arctan (\frac{1}{2}) + 18 0^{\circ} n

Soluciones para el rango

0 \leq x \leq 36 0^{\circ}

x = arctan (\frac{1}{2}), x = arctan (\frac{1}{2}) + 18 0^{\circ}

Mostrar soluciones en forma decimal

x = 0.46364 \dots, x = 0.46364 \dots + 18 0^{\circ}

8 tan (A) + 3 = 2 tan (A) + 3

cosh (x) = 3

2 sec (x) + 1 = 0

cot (x) = - 3

2 cos (x) - cos (x) sin (x) = 0