2sin(x + 15°)= 1,462

asked by guest
on Nov 21, 2024 at 9:47 am



You asked:

Solve the equation 2sin(x+15)=1,4622 \sin\left( x + 15^{\circ} \right) = 1,462 for the variable xx.

MathBot Answer:

There are no real solutions.


The complex solutions are: x={2πnilog(10687212924133590)2+arctan(73127316+466795+12222657316466795+1222265+7312)  |  nZ}{6.2831853n+1.3089969+7.2875602i  |  nZ}x={arctan(466795+1222265+7312+731673161222265+466795+7312)+2πnilog(1068721+2924133590)2  |  nZ}{6.2831853n+1.30899697.2875602i  |  nZ}\begin{aligned}x &= \left\{2 \pi n - \frac{i \log{\left(1068721 - 2924 \sqrt{133590} \right)}}{2} + \arctan{\left(\frac{- 731 \sqrt{2} - 731 \sqrt{6} + 4 \sqrt{66795} + 12 \sqrt{22265}}{- 731 \sqrt{6} - 4 \sqrt{66795} + 12 \sqrt{22265} + 731 \sqrt{2}} \right)}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 1.3089969 + 7.2875602 i\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{- \arctan{\left(\frac{4 \sqrt{66795} + 12 \sqrt{22265} + 731 \sqrt{2} + 731 \sqrt{6}}{- 731 \sqrt{6} - 12 \sqrt{22265} + 4 \sqrt{66795} + 731 \sqrt{2}} \right)} + 2 \pi n - \frac{i \log{\left(1068721 + 2924 \sqrt{133590} \right)}}{2}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 1.3089969 - 7.2875602 i\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}


ii is the imaginary unit, defined as i2=1i^2 = -1.