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2sen(x)cos(x)+cos(x)=02 space s e n space open paren x close paren cosine x plus cosine x equals 0

sen2(x)=1−2cos(x)+cos2(x)s e n space squared open paren x close paren equals 1 minus 2 cosine x plus cosine squared x Sustituimos

| Ecuación | Solución General | Solución en $[0, 2\pi)$ | | :--- | :--- | :--- | | $\sin(x) = k$ | $x = \arcsin(k) + 2\pi n$ $x = \pi - \arcsin(k) + 2\pi n$ | $x_1 = \arcsin(k)$ $x_2 = \pi - x_1$ | | $\cos(x) = k$ | $x = \pm \arccos(k) + 2\pi n$ | $x_1 = \arccos(k)$ $x_2 = 2\pi - x_1$ | | $\tan(x) = k$ | $x = \arctan(k) + \pi n$ | $x = \arctan(k)$ (y sumas $\pi$ si cabe) |

2 sine x plus 1 equals 0 right arrow sine x equals negative 0.5 right arrow bold x equals 210 raised to the composed with power comma 330 raised to the composed with power (Q3 and Q4). 3. Equations with Tangents Isolate the tangent.

Answer: ( x = \frac\pi2,\ \frac7\pi6,\ \frac11\pi6 ).

: [ x = \frac\pi2 + 2k\pi, \quad x = \frac7\pi6 + 2k\pi, \quad x = \frac11\pi6 + 2k\pi ]

Solve ( \cos 2x = \cos x ) for ( x \in [0, 2\pi) ).

Mastering trigonometric equations in 1º Bachillerato requires:

Resolvemos la ecuación de segundo grado usando la fórmula general: Obtenemos dos resultados: Ahora deshacemos el cambio de variable: . El único ángulo entre 360∘360 raised to the composed with power que cumple esto es Caso 2:

Ecuaciones Trigonometricas 1 Bachillerato Ejercicios Resueltos Fixed

2sen(x)cos(x)+cos(x)=02 space s e n space open paren x close paren cosine x plus cosine x equals 0

sen2(x)=1−2cos(x)+cos2(x)s e n space squared open paren x close paren equals 1 minus 2 cosine x plus cosine squared x Sustituimos

| Ecuación | Solución General | Solución en $[0, 2\pi)$ | | :--- | :--- | :--- | | $\sin(x) = k$ | $x = \arcsin(k) + 2\pi n$ $x = \pi - \arcsin(k) + 2\pi n$ | $x_1 = \arcsin(k)$ $x_2 = \pi - x_1$ | | $\cos(x) = k$ | $x = \pm \arccos(k) + 2\pi n$ | $x_1 = \arccos(k)$ $x_2 = 2\pi - x_1$ | | $\tan(x) = k$ | $x = \arctan(k) + \pi n$ | $x = \arctan(k)$ (y sumas $\pi$ si cabe) | 2sen(x)cos(x)+cos(x)=02 space s e n space open paren

2 sine x plus 1 equals 0 right arrow sine x equals negative 0.5 right arrow bold x equals 210 raised to the composed with power comma 330 raised to the composed with power (Q3 and Q4). 3. Equations with Tangents Isolate the tangent.

Answer: ( x = \frac\pi2,\ \frac7\pi6,\ \frac11\pi6 ). Answer: ( x = \frac\pi2,\ \frac7\pi6,\ \frac11\pi6 )

: [ x = \frac\pi2 + 2k\pi, \quad x = \frac7\pi6 + 2k\pi, \quad x = \frac11\pi6 + 2k\pi ]

Solve ( \cos 2x = \cos x ) for ( x \in [0, 2\pi) ). El único ángulo entre 360∘360 raised to the

Mastering trigonometric equations in 1º Bachillerato requires:

Resolvemos la ecuación de segundo grado usando la fórmula general: Obtenemos dos resultados: Ahora deshacemos el cambio de variable: . El único ángulo entre 360∘360 raised to the composed with power que cumple esto es Caso 2: