What is the general solution for 3sin(θ)+1=1 ?

The general solution for 3sin(θ)+1=1 is θ=2pin,θ=pi+2pin

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3sin(θ)+1=1

3 sin (θ) + 1 = 1

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 sin (θ) + 1 = 1

Subtract

1

from both sides

3 sin (θ) + 1 - 1 = 1 - 1

Simplify

3 sin (θ) = 0

Divide both sides by

3

3 sin (θ) = 0

Divide both sides by

3

\frac{3 sin ( θ )}{3} = \frac{0}{3}

Simplify

sin (θ) = 0

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

csc^{2} (x) - 3 csc (x) - 4 = 0

3 cos (x) = 2

4 tan (θ) + 1 = 0

0 = - 3 sin (x)

5 sin (x) - 1 = 0

What is the general solution for 3sin(θ)+1=1 ?
The general solution for 3sin(θ)+1=1 is θ=2pin,θ=pi+2pin