sin(x) = 1.5 * sin(3x - 180°)

asked by guest
on Oct 20, 2024 at 2:42 pm



You asked:

Solve the equation \(\sin\left( x \right) = 1.5 \cdot \sin\left( 3 x - 180^{\circ} \right)\) for the variable \(x\).

MathBot Answer:

The real solutions are: \[\begin{aligned}x &= \left\{2 \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\pi \left(1 + 2 n\right)\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 3.1415927\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\frac{\pi}{2} - \frac{\arctan{\left(\frac{\sqrt{11}}{5} \right)}}{2} + 2 \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 1.2779536\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\frac{\arctan{\left(\frac{\sqrt{11}}{5} \right)}}{2} + \frac{3 \pi}{2} + 2 \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 5.0052318\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\frac{\pi}{2} + \frac{\arctan{\left(\frac{\sqrt{11}}{5} \right)}}{2} + 2 \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 1.8636391\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{- \frac{\arctan{\left(\frac{\sqrt{11}}{5} \right)}}{2} + \frac{3 \pi}{2} + 2 \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 4.4195462\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]

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