Ecuaciones Trigonometricas 1 Bachillerato [verified] May 2026

Let ( t = 2x ). Solve ( \tan t = 1 ). Principal value: ( t = \pi/4 ). Tangent period is ( \pi ): ( t = \pi/4 + k\pi ). Thus ( 2x = \pi/4 + k\pi \Rightarrow x = \pi/8 + k\pi/2 ).

( \pi/8,\ 5\pi/8,\ 9\pi/8,\ 13\pi/8 ). Type 5: Equation with sine and cosine of the same angle Example: ( \sin x = \cos x ). ecuaciones trigonometricas 1 bachillerato

Find ( k ) for ( 0 \le x < 2\pi ): ( k=0 \to \pi/8 ) ( k=1 \to \pi/8 + \pi/2 = 5\pi/8 ) ( k=2 \to 9\pi/8 ) ( k=3 \to 13\pi/8 ) ( k=4 \to 17\pi/8 = 2\pi + \pi/8 ) (too large). Let ( t = 2x )