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

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

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

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

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

Solution steps

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

Simplify

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

- \frac{1}{2}

Multiply by the conjugate

\frac{2}{2}

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

1 \cdot 2 = 2

22 = 2

22

Apply radical rule:

a a = a

22 = 2

= 2

= - \frac{2}{2}

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

General solutions for

sin (a) = - \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}

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

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

5 cos (x) - 2 sin (x) = 0.5

sin (x) = \frac{6}{15}

cot (θ) = 1.4

tan (x) = 0, x

3 ∣ sin (3 x) ∣ = 0

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