5sin^2\theta =4cos^2\theta

asked by guest
on Nov 19, 2024 at 6:49 am



You asked:

Solve the equation \(5 \cdot {\sin\left( θ \right)}^{2} = 4 \cdot {\cos\left( θ \right)}^{2}\) for the variable \(θ\).

MathBot Answer:

The real solutions are: \[\begin{aligned}θ &= \left\{\frac{\arctan{\left(4 \sqrt{5} \right)}}{2} + 2 \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 0.72972766\; \middle|\; n \in \mathbb{Z}\right\}\\θ &= \left\{\pi - \frac{\arctan{\left(4 \sqrt{5} \right)}}{2} + 2 \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 2.411865\; \middle|\; n \in \mathbb{Z}\right\}\\θ &= \left\{\pi + \frac{\arctan{\left(4 \sqrt{5} \right)}}{2} + 2 \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 3.8713203\; \middle|\; n \in \mathbb{Z}\right\}\\θ &= \left\{2 \pi - \frac{\arctan{\left(4 \sqrt{5} \right)}}{2} + 2 \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 5.5534576\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]

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