What is the general solution for sin(x)=(2*490*10^{-9})/(151*10^{-6)} ?

The general solution for sin(x)=(2*490*10^{-9})/(151*10^{-6)} is x=0.00649…+2pin,x=pi-0.00649…+2pin

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sin(x)=(249010^{-9})/(151*10^{-6)}

sin (x) = \frac{2 \cdot 490 \cdot 1 0 ^{- 9}}{151 \cdot 1 0 ^{- 6}}

x = 0.00649 \dots + 2 πn, x = π - 0.00649 \dots + 2 πn

Radians

x = 0.00649 \dots + 6.28318 \dots n, x = π - 0.00649 \dots + 6.28318 \dots n

Solution steps

sin (x) = \frac{2 \cdot 490 \cdot 1 0 ^{- 9}}{151 \cdot 1 0 ^{- 6}}

Simplify

\frac{2 \cdot 490 \cdot 1 0 ^{- 9}}{151 \cdot 1 0 ^{- 6}} : \frac{49}{7550}

\frac{2 \cdot 490 \cdot 1 0 ^{- 9}}{151 \cdot 1 0 ^{- 6}}

Multiply the numbers:

2 \cdot 490 = 980

= \frac{1 0 ^{- 9} \cdot 980}{1 0 ^{- 6} \cdot 151}

Cancel

\frac{980 \cdot 1 0 ^{- 9}}{151 \cdot 1 0 ^{- 6}} : \frac{980}{1 0 ^{3} \cdot 151}

\frac{980 \cdot 1 0 ^{- 9}}{151 \cdot 1 0 ^{- 6}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{1 0 ^{- 9}}{1 0 ^{- 6}} = \frac{1}{1 0 ^{- 6 - (- 9)}}

= \frac{980}{151 \cdot 1 0 ^{- 6 - (- 9)}}

Subtract the numbers:

- 6 - (- 9) = 3

= \frac{980}{1 0 ^{3} \cdot 151}

= \frac{980}{1 0 ^{3} \cdot 151}

Factor

980 : 2^{2} \cdot 7^{2} \cdot 5

Factor

980 = 2^{2} \cdot 7^{2} \cdot 5

Factor

1 0^{3} : 2^{3} \cdot 5^{3}

Factor

10 = 2 \cdot 5

= (2 \cdot 5)^{3}

Apply exponent rule:

(ab)^{c} = a^{c} b^{c}

= 2^{3} \cdot 5^{3}

= \frac{2 ^{2} \cdot 7 ^{2} \cdot 5}{2 ^{3} \cdot 5 ^{3} \cdot 151}

Cancel

\frac{2 ^{2} \cdot 5 \cdot 7 ^{2}}{2 ^{3} \cdot 5 ^{3} \cdot 151} : \frac{7 ^{2}}{5 ^{2} \cdot 2 \cdot 151}

\frac{2 ^{2} \cdot 5 \cdot 7 ^{2}}{2 ^{3} \cdot 5 ^{3} \cdot 151}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{2 ^{2}}{2 ^{3}} = \frac{1}{2 ^{3 - 2}}

= \frac{7 ^{2} \cdot 5}{5 ^{3} \cdot 151 \cdot 2 ^{3 - 2}}

Subtract the numbers:

3 - 2 = 1

= \frac{7 ^{2} \cdot 5}{5 ^{3} \cdot 2 \cdot 151}

Cancel the common factor:

5

= \frac{7 ^{2}}{5 ^{2} \cdot 2 \cdot 151}

= \frac{7 ^{2}}{5 ^{2} \cdot 2 \cdot 151}

Multiply the numbers:

2 \cdot 151 = 302

= \frac{7 ^{2}}{5 ^{2} \cdot 302}

7^{2} = 49

= \frac{49}{5 ^{2} \cdot 302}

302 \cdot 5^{2} = 7550

302 \cdot 5^{2}

5^{2} = 25

= 302 \cdot 25

Multiply the numbers:

302 \cdot 25 = 7550

= 7550

= \frac{49}{7550}

Apply trig inverse properties

sin (x) = \frac{49}{7550}

General solutions for

sin (x) = \frac{49}{7550}

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

x = arcsin (\frac{49}{7550}) + 2 πn, x = π - arcsin (\frac{49}{7550}) + 2 πn

x = arcsin (\frac{49}{7550}) + 2 πn, x = π - arcsin (\frac{49}{7550}) + 2 πn

Show solutions in decimal form

x = 0.00649 \dots + 2 πn, x = π - 0.00649 \dots + 2 πn

cos (\frac{x}{2}) - cos (x) = 0

cos (2 t) = cos (t), 0 \leq t < 2 π

(cos (2 x))^{2} = cos (x)

sin (θ) = sin (- \frac{2 π}{3})

sin (x) = (\frac{23}{24})

What is the general solution for sin(x)=(2*490*10^{-9})/(151*10^{-6)} ?
The general solution for sin(x)=(2*490*10^{-9})/(151*10^{-6)} is x=0.00649…+2pin,x=pi-0.00649…+2pin