What is the general solution for 2-6.5sin(x)=0 ?

The general solution for 2-6.5sin(x)=0 is x=0.31276…+2pin,x=pi-0.31276…+2pin

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Popular >

2-6.5sin(x)=0

Solution

2 - 6.5 sin (x) = 0

Solution

x = 0.31276 \dots + 2 πn, x = π - 0.31276 \dots + 2 πn

Degrees

x = 17.92021 \dots^{\circ} + 36 0^{\circ} n, x = 162.07978 \dots^{\circ} + 36 0^{\circ} n

Solution steps

2 - 6.5 sin (x) = 0

Multiply both sides by

10

2 - 6.5 sin (x) = 0

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere is one digit to the right of the decimal point, therefore multiply by

10

2 \cdot 10 - 6.5 sin (x) \cdot 10 = 0 \cdot 10

Refine

20 - 65 sin (x) = 0

20 - 65 sin (x) = 0

Move

20

to the right side

20 - 65 sin (x) = 0

Subtract

20

from both sides

20 - 65 sin (x) - 20 = 0 - 20

Simplify

- 65 sin (x) = - 20

- 65 sin (x) = - 20

Divide both sides by

- 65

- 65 sin (x) = - 20

Divide both sides by

- 65

\frac{- 65 sin ( x )}{- 65} = \frac{- 20}{- 65}

Simplify

\frac{- 65 sin ( x )}{- 65} = \frac{- 20}{- 65}

Simplify

\frac{- 65 sin ( x )}{- 65} : sin (x)

\frac{- 65 sin ( x )}{- 65}

Apply the fraction rule:

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

= \frac{65 sin ( x )}{65}

Divide the numbers:

\frac{65}{65} = 1

= sin (x)

Simplify

\frac{- 20}{- 65} : \frac{4}{13}

\frac{- 20}{- 65}

Apply the fraction rule:

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

= \frac{20}{65}

Cancel the common factor:

5

= \frac{4}{13}

sin (x) = \frac{4}{13}

sin (x) = \frac{4}{13}

sin (x) = \frac{4}{13}

Apply trig inverse properties

sin (x) = \frac{4}{13}

General solutions for

sin (x) = \frac{4}{13}

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

x = arcsin (\frac{4}{13}) + 2 πn, x = π - arcsin (\frac{4}{13}) + 2 πn

x = arcsin (\frac{4}{13}) + 2 πn, x = π - arcsin (\frac{4}{13}) + 2 πn

Show solutions in decimal form

x = 0.31276 \dots + 2 πn, x = π - 0.31276 \dots + 2 πn

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1.33 \cdot sin (6 0^{\circ}) = 1.52 \cdot sin (x)

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Frequently Asked Questions (FAQ)

What is the general solution for 2-6.5sin(x)=0 ?
The general solution for 2-6.5sin(x)=0 is x=0.31276…+2pin,x=pi-0.31276…+2pin