t=−(-3)±(-3)2−4⋅2⋅12⋅2=3±9−84=3±14t equals the fraction with numerator negative open paren negative 3 close paren plus or minus the square root of open paren negative 3 close paren squared minus 4 center dot 2 center dot 1 end-root and denominator 2 center dot 2 end-fraction equals the fraction with numerator 3 plus or minus the square root of 9 minus 8 end-root and denominator 4 end-fraction equals the fraction with numerator 3 plus or minus 1 and denominator 4 end-fraction Deshacemos el cambio de variable para encontrar
Aplicamos la raíz cuadrada a ambos lados (¡no olvides el doble signo ±plus or minus
: Let (t = \sin x). Then (2t^2 - t - 1 = 0).
I need to ensure the Spanish is natural and educational, using terms like "ángulos," "razones trigonométricas," "seno," "coseno," "tangente," "solución general," "primer y segundo cuadrante," etc. I'll include examples with clear steps, showing how to reduce to elementary equations and find all solutions in [0, 2π) or general solutions with +2kπ. I'll also mention common pitfalls like extraneous solutions when squaring or dividing by sine/cosine. I'll include examples with clear steps, showing how
¿Qué ángulos tienen tangente (\sqrt3)? [ \tan x = \sqrt3 \Rightarrow x = 60^\circ = \frac\pi3 \ \texty \ x = 240^\circ = \frac4\pi3 ] Pero la tangente tiene periodo (\pi), así que: [ x = \frac\pi3 + k\pi ]
¿Qué tipo de ecuación trigonométrica te resulta más difícil resolver actualmente? Si me lo indicas, puedo prepararte centrados en ángulos dobles , sistemas de ecuaciones o fórmulas de adición . Share public link
2−2sin2x+3sinx=32 minus 2 sine squared x plus 3 sine x equals 3 2. Reordenar como ecuación cuadrática [ \tan x = \sqrt3 \Rightarrow x =
Repiten sus valores cada vuelta completa, es decir, cada 360∘360 raised to the composed with power radianes. Las soluciones se expresan sumando +360∘kpositive 360 raised to the composed with power k
cos2(x)=(1−sin(x))2cosine squared x equals open paren 1 minus sine x close paren squared
Recuerda que la tangente no existe para 90∘90 raised to the composed with power 270∘270 raised to the composed with power . Si tu solución es una de estas, descalcártala. puedo prepararte centrados en ángulos dobles
Caso 1: ( \cos x = 1 ) → ( x = 0, 2\pi ) (pero ( 2\pi ) coincide con 0 en intervalo cerrado? Normalmente damos 0 y ( 2\pi ) si es cerrado).
[ 2\cos^2 x - 3\cos x + 1 = 0 ]