What is the general solution for 2sin(θ)+5=6 ?

The general solution for 2sin(θ)+5=6 is θ= pi/6+2pin,θ=(5pi)/6+2pin

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2sin(θ)+5=6

2 sin (θ) + 5 = 6

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

Degrees

θ = 3 0^{\circ} + 36 0^{\circ} n, θ = 15 0^{\circ} + 36 0^{\circ} n

Solution steps

2 sin (θ) + 5 = 6

Move

5

to the right side

2 sin (θ) + 5 = 6

Subtract

5

from both sides

2 sin (θ) + 5 - 5 = 6 - 5

Simplify

2 sin (θ) = 1

2 sin (θ) = 1

Divide both sides by

2

2 sin (θ) = 1

Divide both sides by

2

\frac{2 sin ( θ )}{2} = \frac{1}{2}

Simplify

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{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

x, cos (x) = \frac{1}{2}

2 sin (2 x) + 3 = 0

20 sin (x) + 3 = 8

cos (2 θ) + 3 = 5 cos (θ)

cos (5 x) = \frac{3}{2}

What is the general solution for 2sin(θ)+5=6 ?
The general solution for 2sin(θ)+5=6 is θ= pi/6+2pin,θ=(5pi)/6+2pin