What is the general solution for sin(x)=(-1}{\frac{sqrt(5))/2} ?

The general solution for sin(x)=(-1}{\frac{sqrt(5))/2} is x=-1.10714…+2pin,x=pi+1.10714…+2pin

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sin(x)=(-1}{\frac{sqrt(5))/2}

sin (x) = \frac{- 1}{\frac{5}{2}}

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

Solution steps

sin (x) = \frac{- 1}{\frac{5}{2}}

Simplify

\frac{- 1}{\frac{5}{2}} : - \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

2 csc^{2} (θ) - 3 cot (θ) + 3 = 0

\frac{2 sin ( x ) + 1}{cos ( x )} = 0

sin (x) = 0.03725

tan (x) = 2.747

y, \frac{sin ( 3 y )}{3} = \frac{cos ( 2 x )}{2} + \frac{1}{2}

What is the general solution for sin(x)=(-1}{\frac{sqrt(5))/2} ?
The general solution for sin(x)=(-1}{\frac{sqrt(5))/2} is x=-1.10714…+2pin,x=pi+1.10714…+2pin