solve sin ^2x =4

asked by guest
on Nov 26, 2024 at 9:40 am



You asked:

Solve the equation \({\sin\left( x \right)}^{2} = 4\) for the variable \(x\).

MathBot Answer:

There are no real solutions.

The complex solutions are: \[\begin{aligned}x &= \left\{\frac{\pi}{2} + 2 \pi n - \frac{i \log{\left(7 - 4 \sqrt{3} \right)}}{2}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 1.5707963 + 1.3169579 i\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\frac{\pi}{2} + 2 \pi n - \frac{i \log{\left(7 + 4 \sqrt{3} \right)}}{2}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 1.5707963 - 1.3169579 i\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\frac{3 \pi}{2} + 2 \pi n - \frac{i \log{\left(7 - 4 \sqrt{3} \right)}}{2}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 4.712389 + 1.3169579 i\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\frac{3 \pi}{2} + 2 \pi n - \frac{i \log{\left(7 + 4 \sqrt{3} \right)}}{2}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 4.712389 - 1.3169579 i\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]

\(i\) is the imaginary unit, defined as \(i^2 = -1\).

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