sin(3x-6)=cos(6x-3)

asked by guest
on Nov 18, 2024 at 4:32 am



You asked:

Solve the equation \(\sin\left( 3 x - 6 \right) = \cos\left( 6 x - 3 \right)\) for the variable \(x\).

MathBot Answer:

The real solutions are: \[\begin{aligned}x &= \left\{1 - \frac{\pi}{6} + \frac{2 \pi n}{3}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{2.0943951 n + 0.47640122\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{-1 + \frac{\pi}{2} + \frac{2 \pi n}{3}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{2.0943951 n + 0.57079633\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{1 + \frac{\pi}{18} + \frac{2 \pi n}{3}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{2.0943951 n + 1.1745329\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{- \frac{\arctan{\left(\frac{1}{\tan{\left(3 + \frac{\pi}{3} \right)}} \right)}}{3} + \frac{2 \pi}{3} + \frac{2 \pi n}{3}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{2.0943951 n + 1.8726646\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]

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