What is the general solution for sin(θ)=-2/(sqrt(2)) ?

The general solution for sin(θ)=-2/(sqrt(2)) is No Solution for θ\in\mathbb{R}

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sin(θ)=-2/(sqrt(2))

sin (θ) = - \frac{2}{2}

No Solution for θ \in R

Solution steps

sin (θ) = - \frac{2}{2}

Simplify

- \frac{2}{2} : - 2

- \frac{2}{2}

Apply radical rule:

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

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

Apply exponent rule:

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

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

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

Subtract the numbers:

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

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

Apply radical rule:

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

= - 2

- 1 \leq sin (x) \leq 1

No Solution for θ \in R

What is the general solution for sin(θ)=-2/(sqrt(2)) ?
The general solution for sin(θ)=-2/(sqrt(2)) is No Solution for θ\in\mathbb{R}