What is the general solution for csc(θ)=(sqrt(28))/2 ,sin(θ) ?

The general solution for csc(θ)=(sqrt(28))/2 ,sin(θ) is No Solution for θ\in\mathbb{R}

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csc(θ)=(sqrt(28))/2 ,sin(θ)

csc (θ) = \frac{28}{2}, sin (θ)

No Solution for θ \in R

Solution steps

csc (θ) = \frac{28}{2}, sin (θ)

Simplify

\frac{28}{2} : 7

\frac{28}{2}

Factor

28 : 27

Factor

28 = 2^{2} \cdot 7

= 2^{2} \cdot 7

Apply radical rule:

= 7 2^{2}

Simplify

2^{2} : 2

2^{2}

Apply radical rule:

assuming

a \geq 0

= 2

= 27

= \frac{2 7}{2}

Divide the numbers:

\frac{2}{2} = 1

= 7

Apply trig inverse properties

csc (θ) = 7

General solutions for

csc (θ) = 7

csc (x) = a \Rightarrow x = arccsc (a) + 2 πn, x = π - arccsc (a) + 2 πn

θ = arccsc (7) + 2 πn, θ = π - arccsc (7) + 2 πn

θ = arccsc (7) + 2 πn, θ = π - arccsc (7) + 2 πn

Solutions for the range

sin (θ)

No Solution for θ \in R

\frac{1 + csc ( γ )}{cot ( γ ) + cos ( γ )} = csc (γ)

sin (θ) = \frac{2}{6}

3 sin (2 x) = - 2

x, arctan (y) = 2 arctan (x)

sin (2 x) = - \frac{3}{2}

What is the general solution for csc(θ)=(sqrt(28))/2 ,sin(θ) ?
The general solution for csc(θ)=(sqrt(28))/2 ,sin(θ) is No Solution for θ\in\mathbb{R}