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

The general solution for 3+3sin(θ)=3-3sin(θ) is θ=2pin,θ=pi+2pin

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3+3sin(θ)=3-3sin(θ)

3 + 3 sin (θ) = 3 - 3 sin (θ)

θ = 2 πn, θ = π + 2 πn

Degrees

θ = 0^{\circ} + 36 0^{\circ} n, θ = 18 0^{\circ} + 36 0^{\circ} n

Solution steps

3 + 3 sin (θ) = 3 - 3 sin (θ)

Solve by substitution

3 + 3 sin (θ) = 3 - 3 sin (θ)

Let:

sin (θ) = u

3 + 3 u = 3 - 3 u

3 + 3 u = 3 - 3 u : u = 0

3 + 3 u = 3 - 3 u

Subtract

3

from both sides

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

Simplify

3 u = - 3 u

Move

3 u

to the left side

3 u = - 3 u

Add

3 u

to both sides

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

Simplify

6 u = 0

6 u = 0

Divide both sides by

6

6 u = 0

Divide both sides by

6

\frac{6 u}{6} = \frac{0}{6}

Simplify

u = 0

u = 0

Substitute back

u = sin (θ)

sin (θ) = 0

sin (θ) = 0

sin (θ) = 0 : θ = 2 πn, θ = π + 2 πn

sin (θ) = 0

General solutions for

sin (θ) = 0

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 = 0 + 2 πn, θ = π + 2 πn

θ = 0 + 2 πn, θ = π + 2 πn

Solve

θ = 0 + 2 πn : θ = 2 πn

θ = 0 + 2 πn

0 + 2 πn = 2 πn

θ = 2 πn

θ = 2 πn, θ = π + 2 πn

Combine all the solutions

θ = 2 πn, θ = π + 2 πn

\frac{sin ( C )}{18} = \frac{sin ( 6 3 ^{\circ} )}{17}

cos (\frac{1}{2} x) = - 1

\frac{- ( 3 \cdot cos ( Q ^{1} ) )}{2} = 0

tan^{2} (x) + 3 tan (x) = 0, 0^{\circ} \leq x < 36 0^{\circ}

\frac{1}{2} (6.50941) + cos (θ) (10.40478) = 12

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