tan(x)=±3tangent x equals plus or minus the square root of 3 end-root Analizamos ambas posibilidades: El ángulo del primer cuadrante es 60∘60 raised to the composed with power . Como la tangente tiene periodo de 180∘180 raised to the composed with power , la solución general es: Caso negativo: El ángulo del segundo cuadrante equivalente es . Su solución general es: Consejos para repasar antes del examen
Resuelve ( \sqrt3 \tg x - 1 = 0 )
| 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) | tan(x)=±3tangent x equals plus or minus the square
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Here is a breakdown of the essential strategies and three classic solved exercises to help you practice. Key Tools to Remember Fundamental Identity: Double Angle: Always remember that sine and cosine repeat every 360 raised to the composed with power Solved Exercises 1. Using the Fundamental Identity Get everything in terms of the same function. Use Arrange into a quadratic equation (
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cos(2x)=cos2(x)−sin2(x)cosine 2 x equals cosine squared x minus sine squared x 2. Ejercicios Resueltos Paso a Paso Ejercicio 1: Ecuación mediante cambio de variable Resuelve la ecuación en el intervalo Paso 1: Homogeneizar la ecuación Utilizamos la identidad fundamental para dejar toda la ecuación en función del seno: