What is the general solution for 2sin(x-10)=-0.4 ?

The general solution for 2sin(x-10)=-0.4 is x=-0.20135…+360n+10,x=180+0.20135…+360n+10

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Popular Trigonometry >

2sin(x-10)=-0.4

Solution

2 sin (x - 1 0^{\circ}) = - 0.4

Solution

x = - 0.20135 \dots + 36 0^{\circ} n + 1 0^{\circ}, x = 18 0^{\circ} + 0.20135 \dots + 36 0^{\circ} n + 1 0^{\circ}

Radians

x = - 0.20135 \dots + \frac{π}{18} + 2 πn, x = π + 0.20135 \dots + \frac{π}{18} + 2 πn

Solution steps

2 sin (x - 1 0^{\circ}) = - 0.4

Divide both sides by

2

2 sin (x - 1 0^{\circ}) = - 0.4

Divide both sides by

2

\frac{2 sin ( x - 1 0 ^{\circ} )}{2} = \frac{- 0.4}{2}

Simplify

\frac{2 sin ( x - 1 0 ^{\circ} )}{2} = \frac{- 0.4}{2}

Simplify

\frac{2 sin ( x - 1 0 ^{\circ} )}{2} : sin (x - 1 0^{\circ})

\frac{2 sin ( x - 1 0 ^{\circ} )}{2}

Divide the numbers:

\frac{2}{2} = 1

= sin (x - 1 0^{\circ})

Simplify

\frac{- 0.4}{2} : - 0.2

\frac{- 0.4}{2}

Apply the fraction rule:

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

= - \frac{0.4}{2}

Divide the numbers:

\frac{0.4}{2} = 0.2

= - 0.2

sin (x - 1 0^{\circ}) = - 0.2

sin (x - 1 0^{\circ}) = - 0.2

sin (x - 1 0^{\circ}) = - 0.2

Apply trig inverse properties

sin (x - 1 0^{\circ}) = - 0.2

General solutions for

sin (x - 1 0^{\circ}) = - 0.2

sin (x) = - a \Rightarrow x = arcsin (- a) + 36 0^{\circ} n, x = 18 0^{\circ} + arcsin (a) + 36 0^{\circ} n

x - 1 0^{\circ} = arcsin (- 0.2) + 36 0^{\circ} n, x - 1 0^{\circ} = 18 0^{\circ} + arcsin (0.2) + 36 0^{\circ} n

x - 1 0^{\circ} = arcsin (- 0.2) + 36 0^{\circ} n, x - 1 0^{\circ} = 18 0^{\circ} + arcsin (0.2) + 36 0^{\circ} n

Solve

x - 1 0^{\circ} = arcsin (- 0.2) + 36 0^{\circ} n : x = - arcsin (\frac{1}{5}) + 36 0^{\circ} n + 1 0^{\circ}

x - 1 0^{\circ} = arcsin (- 0.2) + 36 0^{\circ} n

Simplify

arcsin (- 0.2) + 36 0^{\circ} n : - arcsin (\frac{1}{5}) + 36 0^{\circ} n

arcsin (- 0.2) + 36 0^{\circ} n

arcsin (- 0.2) = - arcsin (\frac{1}{5})

arcsin (- 0.2)

= arcsin (- \frac{1}{5})

Use the following property:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{1}{5}) = - arcsin (\frac{1}{5})

= - arcsin (\frac{1}{5})

= - arcsin (\frac{1}{5}) + 36 0^{\circ} n

x - 1 0^{\circ} = - arcsin (\frac{1}{5}) + 36 0^{\circ} n

Move

1 0^{\circ}

to the right side

x - 1 0^{\circ} = - arcsin (\frac{1}{5}) + 36 0^{\circ} n

Add

1 0^{\circ}

to both sides

x - 1 0^{\circ} + 1 0^{\circ} = - arcsin (\frac{1}{5}) + 36 0^{\circ} n + 1 0^{\circ}

Simplify

x = - arcsin (\frac{1}{5}) + 36 0^{\circ} n + 1 0^{\circ}

x = - arcsin (\frac{1}{5}) + 36 0^{\circ} n + 1 0^{\circ}

Solve

x - 1 0^{\circ} = 18 0^{\circ} + arcsin (0.2) + 36 0^{\circ} n : x = 18 0^{\circ} + arcsin (0.2) + 36 0^{\circ} n + 1 0^{\circ}

x - 1 0^{\circ} = 18 0^{\circ} + arcsin (0.2) + 36 0^{\circ} n

Move

1 0^{\circ}

to the right side

x - 1 0^{\circ} = 18 0^{\circ} + arcsin (0.2) + 36 0^{\circ} n

Add

1 0^{\circ}

to both sides

x - 1 0^{\circ} + 1 0^{\circ} = 18 0^{\circ} + arcsin (0.2) + 36 0^{\circ} n + 1 0^{\circ}

Simplify

x = 18 0^{\circ} + arcsin (0.2) + 36 0^{\circ} n + 1 0^{\circ}

x = 18 0^{\circ} + arcsin (0.2) + 36 0^{\circ} n + 1 0^{\circ}

x = - arcsin (\frac{1}{5}) + 36 0^{\circ} n + 1 0^{\circ}, x = 18 0^{\circ} + arcsin (0.2) + 36 0^{\circ} n + 1 0^{\circ}

Show solutions in decimal form

x = - 0.20135 \dots + 36 0^{\circ} n + 1 0^{\circ}, x = 18 0^{\circ} + 0.20135 \dots + 36 0^{\circ} n + 1 0^{\circ}

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 2sin(x-10)=-0.4 ?
The general solution for 2sin(x-10)=-0.4 is x=-0.20135…+360n+10,x=180+0.20135…+360n+10