Ecuaciones Trigonometricas 1 Bachillerato Ejercicios Resueltos Fixed __exclusive__ < Direct — Pick >
Trigonometric equations can feel like a maze at first, but once you master the fundamental identities and the unit circle, they become quite logical. At the 1º Bachillerato level, the goal is usually to find all possible solutions within the first lap ( ) or the general solution.
- Basic trigonometric identities
- Solving trigonometric equations using algebraic and trigonometric techniques
- Using trigonometric identities to simplify equations
Step 2: Let ( y = \sin x ): ( 2y^2 - 3y - 2 = 0 ). Discriminant: ( 9 + 16 = 25 ), ( y = \frac3 \pm 54 ).
( y_1 = 2 ) (invalid, sine range [-1,1]), ( y_2 = -\frac12 ). Trigonometric equations can feel like a maze at
Solución (Fixed):
Por lo tanto, las soluciones son x = π/4 + kπ y x = 3π/4 + kπ, donde k es un número entero. Step 2: Let ( y = \sin x ): ( 2y^2 - 3y - 2 = 0 )
. A diferencia de las ecuaciones algebraicas comunes, estas suelen tener múltiples soluciones, e incluso infinitas, debido a la naturaleza periódica de las funciones. sine range [-1
✅ 4. Quick Practice (with answers)
- (\cos x = \frac\sqrt22) → (x = \pi/4 + 2k\pi,\ 7\pi/4 + 2k\pi).
- (2\cos^2 x - 1 = 0) → (\cos^2 x = 1/2 \Rightarrow \cos x = \pm \sqrt2/2) → (x = \pi/4 + k\pi/2) in compact form.
- (\tan x = 1) → (x = \pi/4 + k\pi).
- (\sin x = \cos x) → divide by cos x: (\tan x = 1 \Rightarrow x = \pi/4 + k\pi).
Ejercicio 4: Factorización (Fixed: extraer factor común)
Enunciado: Resuelve: (\sin x \cos x + \sin x = 0)