What is the general solution for solvefor x,z=arcsin(x/y) ?

The general solution for solvefor x,z=arcsin(x/y) is x=sin(z)y

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solvefor x,z=arcsin(x/y)

solve for

x, z = arcsin (\frac{x}{y})

x = sin (z) y

Solution steps

z = arcsin (\frac{x}{y})

Switch sides

arcsin (\frac{x}{y}) = z

Subtract

z

from both sides

arcsin (\frac{x}{y}) - z = 0

Solve by substitution

arcsin (\frac{x}{y}) = z

Let:

u = \frac{x}{y}

arcsin (u) - z = 0

Move

z

to the right side

arcsin (u) = z

Apply trig inverse properties

u = sin (z)

Substitute back

u = \frac{x}{y}

\frac{x}{y} = sin (z) : x = sin (z) y; y \neq = 0

x = sin (z) y

7 tan^{2} (θ) - 11 tan (θ) - 4 = - 8 tan (θ)

2 cos^{2} (2 θ) + sin (2 θ) = 1

8 tan (θ) - 54 = 0

3 sin^{2} (x) - 3 = 0

tan (2 x + \frac{π}{3}) = 3

What is the general solution for solvefor x,z=arcsin(x/y) ?
The general solution for solvefor x,z=arcsin(x/y) is x=sin(z)y