( 0,\ \pi/3,\ \pi,\ 5\pi/3 ). Type 4: Equation with tangent Example: ( \tan(2x) = 1 ) in ( [0, 2\pi) ).
1. What is a Trigonometric Equation? A trigonometric equation is an equation where the unknown variable appears as the argument of one or more trigonometric functions (sine, cosine, tangent, etc.). ecuaciones trigonometricas 1 bachillerato
Bring all terms: ( \sin x \cos x - \frac12\sin x = 0 ) ( \sin x (\cos x - 1/2) = 0 ) ( 0,\ \pi/3,\ \pi,\ 5\pi/3 )
( 2\sin x = 1 ) ( \cos^2 x - \sin^2 x = 0 ) ( \tan(2x) = \sqrt3 ) What is a Trigonometric Equation
With practice, solving trigonometric equations becomes systematic. Memorize the general solution forms and always check your solutions in the original equation.
Method 1: Divide by ( \cos x ) (if ( \cos x \neq 0 )): ( \tan x = 1 \Rightarrow x = \pi/4 + k\pi ). Check ( \cos x = 0 ) gives ( x = \pi/2, 3\pi/2 ), but those don’t satisfy original (sine ≠ cosine). So fine.