sin(x - (2/3)pi) = sin(pi + 2x)

asked by guest
on Nov 15, 2024 at 11:29 am



You asked:

Solve the equation \(\sin\left( x - \frac{2}{3} \cdot \pi \right) = \sin\left( \pi + 2 x \right)\) for the variable \(x\).

MathBot Answer:

The real solutions are: \[\begin{aligned}x &= \left\{2 \pi \left(- \frac{2}{9} + n\right)\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n - 1.3962634\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\frac{\pi \left(1 + 6 n\right)}{3}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 1.0471976\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\frac{2 \pi \left(1 + 9 n\right)}{9}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 0.6981317\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\frac{2 \pi \left(4 + 9 n\right)}{9}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 2.7925268\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]

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