What is the general solution for 4sin(θ)+3sqrt(3)=sqrt(3) ?

The general solution for 4sin(θ)+3sqrt(3)=sqrt(3) is θ=(4pi)/3+2pin,θ=(5pi)/3+2pin

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Popular >

4sin(θ)+3sqrt(3)=sqrt(3)

Solution

4 sin (θ) + 33 = 3

Solution

θ = \frac{4 π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

Degrees

θ = 24 0^{\circ} + 36 0^{\circ} n, θ = 30 0^{\circ} + 36 0^{\circ} n

Solution steps

4 sin (θ) + 33 = 3

Move

33

to the right side

4 sin (θ) + 33 = 3

Subtract

33

from both sides

4 sin (θ) + 33 - 33 = 3 - 33

Simplify

4 sin (θ) + 33 - 33 = 3 - 33

Simplify

4 sin (θ) + 33 - 33 : 4 sin (θ)

4 sin (θ) + 33 - 33

Add similar elements:

33 - 33 = 0

= 4 sin (θ)

Simplify

3 - 33 : - 23

3 - 33

Add similar elements:

3 - 33 = - 23

= - 23

4 sin (θ) = - 23

4 sin (θ) = - 23

4 sin (θ) = - 23

Divide both sides by

4

4 sin (θ) = - 23

Divide both sides by

4

\frac{4 sin ( θ )}{4} = \frac{- 2 3}{4}

Simplify

\frac{4 sin ( θ )}{4} = \frac{- 2 3}{4}

Simplify

\frac{4 sin ( θ )}{4} : sin (θ)

\frac{4 sin ( θ )}{4}

Divide the numbers:

\frac{4}{4} = 1

= sin (θ)

Simplify

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

\frac{- 2 3}{4}

Apply the fraction rule:

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

= - \frac{2 3}{4}

Cancel the common factor:

2

= - \frac{3}{2}

sin (θ) = - \frac{3}{2}

sin (θ) = - \frac{3}{2}

sin (θ) = - \frac{3}{2}

General solutions for

sin (θ) = - \frac{3}{2}

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

θ = \frac{4 π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

θ = \frac{4 π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

Graph

Popular Examples

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cos (2 x) - 2 sin (x) = 0

sin(x)-4cos(x)=0

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2sin(x)+5sqrt(3)=6sqrt(3)

2 sin (x) + 53 = 63

-5*cos(x)-8.6602500000000…*sin(x)=-5

- 5 \cdot cos (x) - 8.6602500000000 \dots \cdot sin (x) = - 5

solvefor y,cos(x)+cos(y)+cos(z)=0 solve for

y, cos (x) + cos (y) + cos (z) = 0

Frequently Asked Questions (FAQ)

What is the general solution for 4sin(θ)+3sqrt(3)=sqrt(3) ?
The general solution for 4sin(θ)+3sqrt(3)=sqrt(3) is θ=(4pi)/3+2pin,θ=(5pi)/3+2pin