What is the general solution for (sqrt(3))/2 =-1/2*sin(θ) ?

The general solution for (sqrt(3))/2 =-1/2*sin(θ) is No Solution for θ\in\mathbb{R}

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(sqrt(3))/2 =-1/2*sin(θ)

\frac{3}{2} = - \frac{1}{2} \cdot sin (θ)

No Solution for θ \in R

Solution steps

\frac{3}{2} = - \frac{1}{2} sin (θ)

Switch sides

- \frac{1}{2} sin (θ) = \frac{3}{2}

Multiply both sides by

- 2

- \frac{1}{2} sin (θ) = \frac{3}{2}

Multiply both sides by

- 2

(- \frac{1}{2} sin (θ)) (- 2) = \frac{3 ( - 2 )}{2}

Simplify

(- \frac{1}{2} sin (θ)) (- 2) = \frac{3 ( - 2 )}{2}

Simplify

(- \frac{1}{2} sin (θ)) (- 2) : sin (θ)

(- \frac{1}{2} sin (θ)) (- 2)

Remove parentheses:

(- a) = - a, - (- a) = a

= \frac{1}{2} sin (θ) \cdot 2

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 2}{2} sin (θ)

Cancel the common factor:

2

= sin (θ) \cdot 1

Multiply:

sin (θ) \cdot 1 = sin (θ)

= sin (θ)

Simplify

\frac{3 ( - 2 )}{2} : - 3

\frac{3 ( - 2 )}{2}

Remove parentheses:

(- a) = - a

= \frac{- 3 \cdot 2}{2}

Apply the fraction rule:

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

= - \frac{3 \cdot 2}{2}

Divide the numbers:

\frac{2}{2} = 1

= - 3

sin (θ) = - 3

sin (θ) = - 3

sin (θ) = - 3

- 1 \leq sin (x) \leq 1

No Solution for θ \in R

sin (θ) = 0.27, 0 \leq θ < 2 π

tan (x) = 0.96

tan (x) = 0.87

4 sec (θ) + 6 = - 2, 0 \leq θ < 2 π

2 sin^{2} (x) - sin (x) = 0

What is the general solution for (sqrt(3))/2 =-1/2*sin(θ) ?
The general solution for (sqrt(3))/2 =-1/2*sin(θ) is No Solution for θ\in\mathbb{R}