What is the general solution for 4sin(θ)+3=1 ?

The general solution for 4sin(θ)+3=1 is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin

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4sin(θ)+3=1

4 sin (θ) + 3 = 1

θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

Degrees

θ = 21 0^{\circ} + 36 0^{\circ} n, θ = 33 0^{\circ} + 36 0^{\circ} n

Solution steps

4 sin (θ) + 3 = 1

Move

3

to the right side

4 sin (θ) + 3 = 1

Subtract

3

from both sides

4 sin (θ) + 3 - 3 = 1 - 3

Simplify

4 sin (θ) = - 2

4 sin (θ) = - 2

Divide both sides by

4

4 sin (θ) = - 2

Divide both sides by

4

\frac{4 sin ( θ )}{4} = \frac{- 2}{4}

Simplify

\frac{4 sin ( θ )}{4} = \frac{- 2}{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}{4} : - \frac{1}{2}

\frac{- 2}{4}

Apply the fraction rule:

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

= - \frac{2}{4}

Cancel the common factor:

2

= - \frac{1}{2}

sin (θ) = - \frac{1}{2}

sin (θ) = - \frac{1}{2}

sin (θ) = - \frac{1}{2}

General solutions for

sin (θ) = - \frac{1}{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{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

25 cot^{2} (θ) - 1 = 0

cos (a) = \frac{5}{13}

sec (2 x) - 2 = 0

2 sin^{2} (θ) + sin (θ) = 1

cot^{2} (x) + csc (x) = 1

What is the general solution for 4sin(θ)+3=1 ?
The general solution for 4sin(θ)+3=1 is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin