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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Popular >

solvefor x,z=arcsin(x/y)

Solution

solve for

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

Solution

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 = 0

Let:

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

u - z = 0

u - z = 0 : u = z

u - z = 0

Move

z

to the right side

u - z = 0

Add

z

to both sides

u - z + z = 0 + z

Simplify

u = z

u = z

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

Substitute back

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

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

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

Let:

u = \frac{x}{y}

arcsin (u) - z = 0

Move

z

to the right side

arcsin (u) - z = 0

Add

z

to both sides

arcsin (u) - z + z = 0 + z

Simplify

arcsin (u) = z

arcsin (u) = z

Apply trig inverse properties

arcsin (u) = z

arcsin (x) = a \Rightarrow x = sin (a)

u = sin (z)

u = sin (z)

Substitute back

u = \frac{x}{y}

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

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

Multiply both sides by

y

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

Multiply both sides by

y

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

Simplify

x = sin (z) y; y \neq = 0

x = sin (z) y; y \neq = 0

x = sin (z) y

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8tan(θ)-sqrt(54)=0

8 tan (θ) - 54 = 0

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

tan(2x+pi/3)=sqrt(3)

tan (2 x + \frac{π}{3}) = 3

Frequently Asked Questions (FAQ)

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