What is the general solution for sin(x)=(6.57*10^{-7})/(1.8*10^{-6)} ?

The general solution for sin(x)=(6.57*10^{-7})/(1.8*10^{-6)} is No Solution for x\in\mathbb{R}

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sin(x)=(6.5710^{-7})/(1.810^{-6)}

sin (x^{\circ}) = \frac{6.57 \cdot 1 0 ^{- 7}}{1.8 \cdot 1 0 ^{- 6}}

No Solution for x \in R

Solution steps

sin (x^{\circ}) = \frac{6.57 \cdot 1 0 ^{- 7}}{1.8 \cdot 1 0 ^{- 6}}

Simplify

\frac{6.57 \cdot 1 0 ^{- 7}}{1.8 \cdot 1 0 ^{- 6}} : \frac{6.57}{18}

\frac{6.57 \cdot 1 0 ^{- 7}}{1.8 \cdot 1 0 ^{- 6}}

Apply exponent rule:

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

\frac{1 0 ^{- 7}}{1 0 ^{- 6}} = \frac{1}{1 0 ^{- 6 - (- 7)}}

= \frac{6.57}{1 0 ^{- 6 - (- 7)} \cdot 1.8}

Subtract the numbers:

- 6 - (- 7) = 1

= \frac{6.57}{10 \cdot 1.8}

Multiply the numbers:

10 \cdot 1.8 = 18

= \frac{6.57}{18}

Apply trig inverse properties

sin (x^{\circ}) = \frac{6.57}{18}

General solutions for

sin (x^{\circ}) = \frac{6.57}{18}

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

x^{\circ} = arcsin (\frac{6.57}{18}) + 2 πn, x^{\circ} = π - arcsin (\frac{6.57}{18}) + 2 πn

x^{\circ} = arcsin (\frac{6.57}{18}) + 2 πn, x^{\circ} = π - arcsin (\frac{6.57}{18}) + 2 πn

No Solution for x \in R

3 sin^{2} (x) + cos^{2} (x) = 3 sin (x)

y, x tan (y) - x^{2} sin (x) + 3 x^{3} = 0

(\frac{( 1 - sin ^{2} ( x ) )}{( 1 + 2 \cdot sin ^{2} ( x ) )}) = 0.45

- 5 sin (t) = 0

4 cos (\frac{θ}{2}) = 3 + 2 cos (θ)

What is the general solution for sin(x)=(6.57*10^{-7})/(1.8*10^{-6)} ?
The general solution for sin(x)=(6.57*10^{-7})/(1.8*10^{-6)} is No Solution for x\in\mathbb{R}