What is the general solution for sin(-x)=-1/3 ,tan(x)=-(sqrt(2))/4 ?

The general solution for sin(-x)=-1/3 ,tan(x)=-(sqrt(2))/4 is No Solution for x\in\mathbb{R}

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Popular >

sin(-x)=-1/3 ,tan(x)=-(sqrt(2))/4

Solution

sin (- x) = - \frac{1}{3}, tan (x) = - \frac{2}{4}

Solution

No Solution for x \in R

Solution steps

sin (- x) = - \frac{1}{3}, tan (x) = - \frac{2}{4}

Apply trig inverse properties

sin (- x) = - \frac{1}{3}

General solutions for

sin (- x) = - \frac{1}{3}

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

- x = arcsin (- \frac{1}{3}) + 2 πn, - x = π + arcsin (\frac{1}{3}) + 2 πn

- x = arcsin (- \frac{1}{3}) + 2 πn, - x = π + arcsin (\frac{1}{3}) + 2 πn

Solve

- x = arcsin (- \frac{1}{3}) + 2 πn : x = arcsin (\frac{1}{3}) - 2 πn

- x = arcsin (- \frac{1}{3}) + 2 πn

Simplify

arcsin (- \frac{1}{3}) + 2 πn : - arcsin (\frac{1}{3}) + 2 πn

arcsin (- \frac{1}{3}) + 2 πn

Use the following property:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{1}{3}) = - arcsin (\frac{1}{3})

= - arcsin (\frac{1}{3}) + 2 πn

- x = - arcsin (\frac{1}{3}) + 2 πn

Divide both sides by

- 1

- x = - arcsin (\frac{1}{3}) + 2 πn

Divide both sides by

- 1

\frac{- x}{- 1} = - \frac{arcsin ( \frac{1}{3} )}{- 1} + \frac{2 πn}{- 1}

Simplify

\frac{- x}{- 1} = - \frac{arcsin ( \frac{1}{3} )}{- 1} + \frac{2 πn}{- 1}

Simplify

\frac{- x}{- 1} : x

\frac{- x}{- 1}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{x}{1}

Apply rule

\frac{a}{1} = a

= x

Simplify

- \frac{arcsin ( \frac{1}{3} )}{- 1} + \frac{2 πn}{- 1} : arcsin (\frac{1}{3}) - 2 πn

- \frac{arcsin ( \frac{1}{3} )}{- 1} + \frac{2 πn}{- 1}

\frac{arcsin ( \frac{1}{3} )}{- 1} = - arcsin (\frac{1}{3})

\frac{arcsin ( \frac{1}{3} )}{- 1}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{arcsin ( \frac{1}{3} )}{1}

Apply the fraction rule:

\frac{a}{1} = a

\frac{arcsin ( \frac{1}{3} )}{1} = arcsin (\frac{1}{3})

= - arcsin (\frac{1}{3})

\frac{2 πn}{- 1} = - 2 πn

\frac{2 πn}{- 1}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{2 πn}{1}

Apply rule

\frac{a}{1} = a

= - 2 πn

= - (- arcsin (\frac{1}{3})) - 2 πn

Apply rule

- (- a) = a

= arcsin (\frac{1}{3}) - 2 πn

x = arcsin (\frac{1}{3}) - 2 πn

x = arcsin (\frac{1}{3}) - 2 πn

x = arcsin (\frac{1}{3}) - 2 πn

Solve

- x = π + arcsin (\frac{1}{3}) + 2 πn : x = - π - arcsin (\frac{1}{3}) - 2 πn

- x = π + arcsin (\frac{1}{3}) + 2 πn

Divide both sides by

- 1

- x = π + arcsin (\frac{1}{3}) + 2 πn

Divide both sides by

- 1

\frac{- x}{- 1} = \frac{π}{- 1} + \frac{arcsin ( \frac{1}{3} )}{- 1} + \frac{2 πn}{- 1}

Simplify

\frac{- x}{- 1} = \frac{π}{- 1} + \frac{arcsin ( \frac{1}{3} )}{- 1} + \frac{2 πn}{- 1}

Simplify

\frac{- x}{- 1} : x

\frac{- x}{- 1}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{x}{1}

Apply rule

\frac{a}{1} = a

= x

Simplify

\frac{π}{- 1} + \frac{arcsin ( \frac{1}{3} )}{- 1} + \frac{2 πn}{- 1} : - π - arcsin (\frac{1}{3}) - 2 πn

\frac{π}{- 1} + \frac{arcsin ( \frac{1}{3} )}{- 1} + \frac{2 πn}{- 1}

\frac{π}{- 1} = - π

\frac{π}{- 1}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{π}{1}

Apply rule

\frac{a}{1} = a

= - π

= - π + \frac{arcsin ( \frac{1}{3} )}{- 1} + \frac{2 πn}{- 1}

\frac{arcsin ( \frac{1}{3} )}{- 1} = - arcsin (\frac{1}{3})

\frac{arcsin ( \frac{1}{3} )}{- 1}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{arcsin ( \frac{1}{3} )}{1}

Apply the fraction rule:

\frac{a}{1} = a

\frac{arcsin ( \frac{1}{3} )}{1} = arcsin (\frac{1}{3})

= - arcsin (\frac{1}{3})

= - π - arcsin (\frac{1}{3}) + \frac{2 πn}{- 1}

\frac{2 πn}{- 1} = - 2 πn

\frac{2 πn}{- 1}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{2 πn}{1}

Apply rule

\frac{a}{1} = a

= - 2 πn

= - π - arcsin (\frac{1}{3}) - 2 πn

x = - π - arcsin (\frac{1}{3}) - 2 πn

x = - π - arcsin (\frac{1}{3}) - 2 πn

x = - π - arcsin (\frac{1}{3}) - 2 πn

x = arcsin (\frac{1}{3}) - 2 πn, x = - π - arcsin (\frac{1}{3}) - 2 πn

Solutions for the range

tan (x) = - \frac{2}{4}

No Solution for x \in R

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Frequently Asked Questions (FAQ)

What is the general solution for sin(-x)=-1/3 ,tan(x)=-(sqrt(2))/4 ?
The general solution for sin(-x)=-1/3 ,tan(x)=-(sqrt(2))/4 is No Solution for x\in\mathbb{R}