What is the general solution for solvefor a,45=arctanh(a/b) ?

The general solution for solvefor a,45=arctanh(a/b) is a=\emptyset b

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Popular >

solvefor a,45=arctanh(a/b)

Solution

solve for

a, 45 = arctanh (\frac{a}{b})

Solution

a = \emptyset b

Solution steps

45 = arctanh (\frac{a}{b})

Switch sides

arctanh (\frac{a}{b}) = 45

Subtract

45

from both sides

arctanh (\frac{a}{b}) - 45 = 0

Solve by substitution

arctanh (\frac{a}{b}) - 45 = 0

Let:

arctanh (\frac{a}{b}) = u

u - 45 = 0

u - 45 = 0 : u = 45

u - 45 = 0

Move

45

to the right side

u - 45 = 0

Add

45

to both sides

u - 45 + 45 = 0 + 45

Simplify

u = 45

u = 45

arctanh (\frac{a}{b}) = 45

Substitute back

u = arctanh (\frac{a}{b})

arctanh (\frac{a}{b}) = 45

arctanh (\frac{a}{b}) = 45

Let:

u = \frac{a}{b}

arctanh (u) - 45 = 0

Solve by substitution

arctanh (u) - 45 = 0

Let:

arctanh (u) = u

u - 45 = 0

u - 45 = 0 : u = 45

u - 45 = 0

Move

45

to the right side

u - 45 = 0

Add

45

to both sides

u - 45 + 45 = 0 + 45

Simplify

u = 45

u = 45

Substitute back

u = arctanh (u)

arctanh (u) = 45

arctanh (u) = 45

Rewrite using trig identities

- 45 + arctanh (u)

Use the Hyperbolic identity:

arctanh (x) = \frac{ln ( \frac{1 + x}{1 - x} )}{2}

= - 45 + \frac{ln ( \frac{1 + u}{1 - u} )}{2}

- 45 + \frac{ln ( \frac{1 + u}{1 - u} )}{2} = 0

Move

45

to the right side

- 45 + \frac{ln ( \frac{1 + u}{1 - u} )}{2} = 0

Add

45

to both sides

- 45 + \frac{ln ( \frac{1 + u}{1 - u} )}{2} + 45 = 0 + 45

Simplify

\frac{ln ( \frac{1 + u}{1 - u} )}{2} = 45

\frac{ln ( \frac{1 + u}{1 - u} )}{2} = 45

Multiply both sides by

2

\frac{ln ( \frac{1 + u}{1 - u} )}{2} = 45

Multiply both sides by

2

\frac{2 ln ( \frac{1 + u}{1 - u} )}{2} = 45 \cdot 2

Simplify

ln (\frac{1 + u}{1 - u}) = 90

ln (\frac{1 + u}{1 - u}) = 90

Apply trig inverse properties

ln (\frac{1 + u}{1 - u}) = 90

General solutions for

ln (\frac{1 + u}{1 - u}) = 90

No Solution

Substitute back

u = \frac{a}{b}

\frac{a}{b} = \emptyset : a = \emptyset b; b \neq = 0

\frac{a}{b} = \emptyset

Multiply both sides by

b

\frac{a}{b} = \emptyset

Multiply both sides by

b

\frac{ab}{b} = \emptyset b; b \neq = 0

Simplify

a = \emptyset b; b \neq = 0

a = \emptyset b; b \neq = 0

a = \emptyset b

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sin(x)= 7/(9.4)

sin (x) = \frac{7}{9.4}

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cos (x) = \frac{6}{11}

Frequently Asked Questions (FAQ)

What is the general solution for solvefor a,45=arctanh(a/b) ?
The general solution for solvefor a,45=arctanh(a/b) is a=\emptyset b