What is the general solution for 3-2sin(θ)=-3+2sin(θ) ?

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

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Popular >

3-2sin(θ)=-3+2sin(θ)

Solution

3 - 2 sin (θ) = - 3 + 2 sin (θ)

Solution

No Solution for θ \in R

Solution steps

3 - 2 sin (θ) = - 3 + 2 sin (θ)

Solve by substitution

3 - 2 sin (θ) = - 3 + 2 sin (θ)

Let:

sin (θ) = u

3 - 2 u = - 3 + 2 u

3 - 2 u = - 3 + 2 u : u = \frac{3}{2}

3 - 2 u = - 3 + 2 u

Move

3

to the right side

3 - 2 u = - 3 + 2 u

Subtract

3

from both sides

3 - 2 u - 3 = - 3 + 2 u - 3

Simplify

- 2 u = 2 u - 6

- 2 u = 2 u - 6

Move

2 u

to the left side

- 2 u = 2 u - 6

Subtract

2 u

from both sides

- 2 u - 2 u = 2 u - 6 - 2 u

Simplify

- 4 u = - 6

- 4 u = - 6

Divide both sides by

- 4

- 4 u = - 6

Divide both sides by

- 4

\frac{- 4 u}{- 4} = \frac{- 6}{- 4}

Simplify

\frac{- 4 u}{- 4} = \frac{- 6}{- 4}

Simplify

\frac{- 4 u}{- 4} : u

\frac{- 4 u}{- 4}

Apply the fraction rule:

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

= \frac{4 u}{4}

Divide the numbers:

\frac{4}{4} = 1

= u

Simplify

\frac{- 6}{- 4} : \frac{3}{2}

\frac{- 6}{- 4}

Apply the fraction rule:

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

= \frac{6}{4}

Cancel the common factor:

2

= \frac{3}{2}

u = \frac{3}{2}

u = \frac{3}{2}

u = \frac{3}{2}

Substitute back

u = sin (θ)

sin (θ) = \frac{3}{2}

sin (θ) = \frac{3}{2}

sin (θ) = \frac{3}{2} :

No Solution

sin (θ) = \frac{3}{2}

- 1 \leq sin (x) \leq 1

No Solution

Combine all the solutions

No Solution for θ \in R

Popular Examples

sin(x)-0.75=0

sin (x) - 0.75 = 0

2cos^2(x)+cos(x)-6=0

2 cos^{2} (x) + cos (x) - 6 = 0

sin(x)=sin(x+1)

sin (x) = sin (x + 1)

1+cos(2x)=sin(2x)

1 + cos (2 x) = sin (2 x)

cos(a)= 6/(7.5)

cos (a) = \frac{6}{7.5}

Frequently Asked Questions (FAQ)

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