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

The general solution for sin(θ)+4=3 is θ=(3pi)/2+2pin

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sin(θ)+4=3

sin (θ) + 4 = 3

θ = \frac{3 π}{2} + 2 πn

Degrees

θ = 27 0^{\circ} + 36 0^{\circ} n

Solution steps

sin (θ) + 4 = 3

Move

4

to the right side

sin (θ) + 4 = 3

Subtract

4

from both sides

sin (θ) + 4 - 4 = 3 - 4

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

cos (3 x) = \frac{1}{3}

sin (θ) = \frac{7}{8}

sin (x) = \frac{- 2}{3}

4 + 4 cos (x) = - 6 cos (x)

2 cos (\frac{x}{2}) = 3, 0 \leq x \leq 2 π

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