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

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

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

tan (2 x - 1) = 0

cos^{2} (x) = \frac{( 4 k - 3 )}{8}

3 cos^{2} (x) - 8 cos (x) + 4 = 0

sin^{(2)} (x) - sin (x) = 1 - sin^{(2)} (x)

49.55 \cdot 1 - sin^{2} (θ) - 30 sin (θ) = 1.225

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