Solve for t (complex solution)
t=-\frac{12i\ln(-\frac{i\sqrt{y^{2}-490y+59400}}{25}-\frac{iy}{25}+\frac{49}{5}i)}{\pi }+24n_{1}-1\text{, }n_{1}\in \mathrm{Z}
t=-\frac{12i\ln(\frac{i\sqrt{y^{2}-490y+59400}}{25}-\frac{iy}{25}+\frac{49}{5}i)}{\pi }+24n_{2}-1\text{, }n_{2}\in \mathrm{Z}
Solve for t
\left\{\begin{matrix}t=\frac{12\arcsin(\frac{245-y}{25})}{\pi }+24n_{1}+23\text{, }n_{1}\in \mathrm{Z}\text{, }&y=270\text{ or }y=220\\t=\frac{12\arcsin(\frac{245-y}{25})}{\pi }+24n_{2}-1\text{, }n_{2}\in \mathrm{Z}\text{; }t=-\frac{12\arcsin(\frac{245-y}{25})}{\pi }+24n_{3}+11\text{, }n_{3}\in \mathrm{Z}\text{, }&y\geq 220\text{ and }y\leq 270\end{matrix}\right.
Solve for y
y=5\left(-5\sin(\frac{\pi \left(t+1\right)}{12})+49\right)
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Trigonometry
5 problems similar to:
y = 245 - 5 \cdot 5 \sin ( \frac { 2 \pi ( t + 1 ) } { 24 } )
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