y = a \cos ( \ln x ) + b \sin ( \ln x
Solve for a
\left\{\begin{matrix}a=-\frac{b\sin(\ln(x))-y}{\cos(\ln(x))}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }x=e^{\pi n_{1}+\frac{\pi }{2}}\text{ and }x>0\\a\in \mathrm{R}\text{, }&y=b\sin(\ln(x))\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }x=e^{\frac{\pi \left(2n_{1}+1\right)}{2}}\end{matrix}\right.
Solve for b
\left\{\begin{matrix}b=-\frac{a\cos(\ln(x))-y}{\sin(\ln(x))}\text{, }&\nexists n_{1}\in \mathrm{Z}\text{ : }x=e^{\pi n_{1}}\text{ and }x>0\\b\in \mathrm{R}\text{, }&y=a\cos(\ln(x))\text{ and }\exists n_{1}\in \mathrm{Z}\text{ : }x=e^{\pi n_{1}}\end{matrix}\right.
Graph
Share
Copied to clipboard
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}