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

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

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3-3sin(θ)=3

3 - 3 sin (θ) = 3

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

Subtract

3

from both sides

3 - 3 sin (θ) - 3 = 3 - 3

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

cos (x) = \frac{10}{26}

x, sin (x) = 5

2 cos (A) = - 2

6 sin (x) + 5 cos (x) = 0

2 cos^{2} (x) - 5 cos (x) + 3 = 0

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