Solve for y
y=\left(\sin(x)+7\right)^{2}
\sin(x)+7\geq 0
Solve for x
x=-\arcsin(\sqrt{y}-7)+2\pi n_{1}+\pi \text{, }n_{1}\in \mathrm{Z}
x=\arcsin(\sqrt{y}-7)+2\pi n_{2}\text{, }n_{2}\in \mathrm{Z}\text{, }y\geq 36\text{ and }y\leq 64
Graph
Share
Copied to clipboard
\sqrt{y}-\sin(x)-\left(-\sin(x)\right)=7-\left(-\sin(x)\right)
Subtract -\sin(x) from both sides of the equation.
\sqrt{y}=7-\left(-\sin(x)\right)
Subtracting -\sin(x) from itself leaves 0.
\sqrt{y}=\sin(x)+7
Subtract -\sin(x) from 7.
y=\left(\sin(x)+7\right)^{2}
Square both sides of the equation.
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}