sin⁴x+cos⁴x=5/8

asked by guest
on Oct 22, 2024 at 2:03 pm



You asked:

Solve the equation \({\sin\left( x \right)}^{4} + {\cos\left( x \right)}^{4} = \frac{5}{8}\) for the variable \(x\).

MathBot Answer:

The real solutions are: \[\begin{aligned}x &= \left\{\frac{2 \pi \left(2 + 3 n\right)}{3}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 4.1887902\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\frac{2 \pi \left(1 + 3 n\right)}{3}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 2.0943951\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\frac{\pi \left(5 + 6 n\right)}{3}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 5.2359878\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\frac{\pi \left(1 + 6 n\right)}{3}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 1.0471976\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\frac{\pi \left(7 + 12 n\right)}{6}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 3.6651914\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\frac{\pi \left(5 + 12 n\right)}{6}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 2.6179939\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\frac{\pi \left(11 + 12 n\right)}{6}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 5.7595865\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\frac{\pi \left(1 + 12 n\right)}{6}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 0.52359878\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]

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