What is the general solution for sin(x)=-1/2 sqrt(2) ?

The general solution for sin(x)=-1/2 sqrt(2) is x=(5pi)/4+2pin,x=(7pi)/4+2pin

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sin(x)=-1/2 sqrt(2)

sin (x) = - \frac{1}{2} 2

x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Solution steps

sin (x) = - \frac{1}{2} 2

Simplify

- \frac{1}{2} 2 : - \frac{2}{2}

- \frac{1}{2} 2

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{1 \cdot 2}{2}

Multiply:

1 \cdot 2 = 2

= - \frac{2}{2}

General solutions for

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

x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

What is the general solution for sin(x)=-1/2 sqrt(2) ?
The general solution for sin(x)=-1/2 sqrt(2) is x=(5pi)/4+2pin,x=(7pi)/4+2pin