Solve for a: cos(.03797a) = -.730756

asked by guest
on Sep 19, 2024 at 9:59 am



You asked:

Solve the equation \[\cos\left( .03797 a \right) = -.730756\] for the unknown \(a\).

MathBot Answer:

The principal value in \(0 \le a \le \frac{100000 \pi}{3797}\) is \(a \approx 62.950358\)

The real solutions are: \[\begin{aligned}a &= \left\{\frac{100000 \pi}{3797} + \frac{100000 \arctan{\left(\frac{9 \sqrt{359564559}}{182689} \right)}}{3797} + \frac{200000 \pi n}{3797}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{165.47762 n + 102.52726\; \middle|\; n \in \mathbb{Z}\right\}\\a &= \left\{- \frac{100000 \arctan{\left(\frac{9 \sqrt{359564559}}{182689} \right)}}{3797} + \frac{100000 \pi}{3797} + \frac{200000 \pi n}{3797}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{165.47762 n + 62.950358\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]

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