Trigonometry-solve-Equation-sin-x-2-2sin-x-3-0-

Question Number 159325 by mnjuly1970 last updated on 15/Nov/21

You can't use 'macro parameter character #' in math mode

s o l v e (E q u a t i o n)

s i n (\frac{x}{2}) - 2 s i n (\frac{x}{3}) = 0

Commented by Ar Brandon last updated on 15/Nov/21

x = 12 π n \pm 12 \arctan (\sqrt{\frac{5}{7} + \frac{4 \sqrt{2}}{7}})

Answered by mr W last updated on 15/Nov/21

\sin (\frac{3 x}{6}) - 2 \sin (\frac{2 x}{6}) = 0

l e t t = \frac{x}{6}

\sin (3 t) - 2 \sin (2 t) = 0

\sin t (3 - 4 \sin^{2} t) - 4 \sin t \cos t = 0

\sin t (4 \cos^{2} t - 4 \cos t - 1) = 0

\sin t = 0 \Rightarrow t = k π \Rightarrow x = 6 k π

4 \cos^{2} t - 4 \cos t - 1 = 0

\cos t = \frac{1 \pm \sqrt{2}}{2} = - \frac{\sqrt{2} - 1}{2} (+ r e j e c t e d)

\Rightarrow t = (2 k + 1) π \pm \cos^{- 1} \frac{\sqrt{2} - 1}{2}

\Rightarrow x = 6 (2 k + 1) π \pm 6 \cos^{- 1} \frac{\sqrt{2} - 1}{2}

Commented by mnjuly1970 last updated on 16/Nov/21

v e r y n i c e s i r W