What is the general solution for sin(x)(5sin(x)+5)=0 ?

The general solution for sin(x)(5sin(x)+5)=0 is x=2pin,x=pi+2pin,x=(3pi)/2+2pin

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

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

x = 2 πn, x = π + 2 πn, x = \frac{3 π}{2} + 2 πn

Degrees

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n

Solution steps

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

Solving each part separately

sin (x) = 0 or 5 sin (x) + 5 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = 0

General solutions for

sin (x) = 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}

x = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 2 πn

Solve

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn, x = π + 2 πn

5 sin (x) + 5 = 0 : x = \frac{3 π}{2} + 2 πn

5 sin (x) + 5 = 0

Move

5

to the right side

5 sin (x) + 5 = 0

Subtract

5

from both sides

5 sin (x) + 5 - 5 = 0 - 5

Simplify

5 sin (x) = - 5

5 sin (x) = - 5

Divide both sides by

5

5 sin (x) = - 5

Divide both sides by

5

\frac{5 sin ( x )}{5} = \frac{- 5}{5}

Simplify

sin (x) = - 1

sin (x) = - 1

General solutions for

sin (x) = - 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}

x = \frac{3 π}{2} + 2 πn

x = \frac{3 π}{2} + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = \frac{3 π}{2} + 2 πn

csc (θ) = \frac{- 3}{5}

sec^{2} (x) + tan^{2} (x) = 5 tan (x)

sin (x) = \frac{9}{12}

- 2 cos (x) + 3 sin (x) = 2

cos (x + \frac{π}{6}) - 1 = cos (x - \frac{π}{6})

What is the general solution for sin(x)(5sin(x)+5)=0 ?
The general solution for sin(x)(5sin(x)+5)=0 is x=2pin,x=pi+2pin,x=(3pi)/2+2pin