What is the general solution for sin(x)=(-2sqrt(5))/5 ?

The general solution for sin(x)=(-2sqrt(5))/5 is x=-1.10714…+2pin,x=pi+1.10714…+2pin

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sin(x)=(-2sqrt(5))/5

sin (x) = \frac{- 2 5}{5}

x = - 1.10714 \dots + 2 πn, x = π + 1.10714 \dots + 2 πn

Degrees

x = - 63.43494 \dots^{\circ} + 36 0^{\circ} n, x = 243.43494 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) = \frac{- 2 5}{5}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

sin (x) = - \frac{2 5}{5}

Apply trig inverse properties

sin (x) = - \frac{2 5}{5}

General solutions for

sin (x) = - \frac{2 5}{5}

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (- \frac{2 5}{5}) + 2 πn, x = π + arcsin (\frac{2 5}{5}) + 2 πn

x = arcsin (- \frac{2 5}{5}) + 2 πn, x = π + arcsin (\frac{2 5}{5}) + 2 πn

Show solutions in decimal form

x = - 1.10714 \dots + 2 πn, x = π + 1.10714 \dots + 2 πn

What is the general solution for sin(x)=(-2sqrt(5))/5 ?
The general solution for sin(x)=(-2sqrt(5))/5 is x=-1.10714…+2pin,x=pi+1.10714…+2pin