What is the general solution for 3+3sin(θ)=0 ?

The general solution for 3+3sin(θ)=0 is θ=(3pi)/2+2pin

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3+3sin(θ)=0

3 + 3 sin (θ) = 0

θ = \frac{3 π}{2} + 2 πn

Degrees

θ = 27 0^{\circ} + 36 0^{\circ} n

Solution steps

3 + 3 sin (θ) = 0

Move

3

to the right side

3 + 3 sin (θ) = 0

Subtract

3

from both sides

3 + 3 sin (θ) - 3 = 0 - 3

Simplify

3 sin (θ) = - 3

3 sin (θ) = - 3

Divide both sides by

3

3 sin (θ) = - 3

Divide both sides by

3

\frac{3 sin ( θ )}{3} = \frac{- 3}{3}

Simplify

sin (θ) = - 1

sin (θ) = - 1

General solutions for

sin (θ) = - 1

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{3 π}{2} + 2 πn

θ = \frac{3 π}{2} + 2 πn

sin (x + \frac{π}{4}) + sin (x - \frac{π}{4}) + \frac{6}{2} = 0

cos (2 x) = \frac{( 8 k - 7 )}{7}

cos^{2} (x) - 3 sin (2 x) + sin^{2} (x) + 2 sin^{2} (2 x) = 0

2 cos^{2} (x) + sin (- x) - 1 = 0

cos (x) = \frac{- 1}{4}

What is the general solution for 3+3sin(θ)=0 ?
The general solution for 3+3sin(θ)=0 is θ=(3pi)/2+2pin