What is the general solution for solvefor 45.6=arcsin((n^1)/(n^2)),n^1 ?

The general solution for solvefor 45.6=arcsin((n^1)/(n^2)),n^1 is n^1=\emptyset n^2

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solvefor 45.6=arcsin((n^1)/(n^2)),n^1

Solution

solve for

45.6 = arcsin (\frac{n ^{1}}{n ^{2}}), n^{1}

Solution

n^{1} = \emptyset n^{2}

Solution steps

45.6 = arcsin (\frac{n ^{1}}{n ^{2}})

Switch sides

arcsin (\frac{n ^{1}}{n ^{2}}) = 45.6

Subtract

45.6

from both sides

arcsin (\frac{n ^{1}}{n ^{2}}) - 45.6 = 0

Solve by substitution

arcsin (\frac{n ^{1}}{n ^{2}}) - 45.6 = 0

Let:

arcsin (\frac{n ^{1}}{n ^{2}}) = u

u - 45.6 = 0

u - 45.6 = 0 : u = 45.6

u - 45.6 = 0

Move

45.6

to the right side

u - 45.6 = 0

Add

45.6

to both sides

u - 45.6 + 45.6 = 0 + 45.6

Simplify

u = 45.6

u = 45.6

arcsin (\frac{n ^{1}}{n ^{2}}) = 45.6

Substitute back

u = arcsin (\frac{n ^{1}}{n ^{2}})

arcsin (\frac{n ^{1}}{n ^{2}}) = 45.6

arcsin (\frac{n ^{1}}{n ^{2}}) = 45.6

Let:

u = \frac{n ^{1}}{n ^{2}}

arcsin (u) - 45.6 = 0

Move

45.6

to the right side

arcsin (u) - 45.6 = 0

Add

45.6

to both sides

arcsin (u) - 45.6 + 45.6 = 0 + 45.6

Simplify

arcsin (u) = 45.6

arcsin (u) = 45.6

- \frac{π}{2} \leq arcsin (x) \leq \frac{π}{2}

No Solution

Substitute back

u = \frac{n ^{1}}{n ^{2}}

\frac{n ^{1}}{n ^{2}} = \emptyset : n^{1} = \emptyset n^{2}; n \neq = 0

\frac{n ^{1}}{n ^{2}} = \emptyset

Multiply both sides by

n^{2}

\frac{n ^{1}}{n ^{2}} = \emptyset

Multiply both sides by

n^{2}

\frac{n ^{1} n ^{2}}{n ^{2}} = \emptyset n^{2}; n \neq = 0

Simplify

n^{1} = \emptyset n^{2}; n \neq = 0

n^{1} = \emptyset n^{2}; n \neq = 0

n^{1} = \emptyset n^{2}

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Frequently Asked Questions (FAQ)

What is the general solution for solvefor 45.6=arcsin((n^1)/(n^2)),n^1 ?
The general solution for solvefor 45.6=arcsin((n^1)/(n^2)),n^1 is n^1=\emptyset n^2