6(sin(x))^2-7cos(x)-8=0

asked by guest
on Sep 21, 2024 at 4:32 am



You asked:

Solve the equation \(6 \cdot {\sin\left( x \right)}^{2} - 7 \cdot \cos\left( x \right) - 8 = 0\) for the variable \(x\).

MathBot Answer:

The real solutions are: \[\begin{aligned}x &= \left\{\frac{2 \pi \left(2 + 3 n\right)}{3}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 4.1887902\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\frac{2 \pi \left(1 + 3 n\right)}{3}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 2.0943951\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\pi + 2 \pi n + \arctan{\left(\frac{\sqrt{5}}{2} \right)}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 3.9826613\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\pi - \arctan{\left(\frac{\sqrt{5}}{2} \right)} + 2 \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 2.300524\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]

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