What is the general solution for sin(x)=(-3)/5 ?

The general solution for sin(x)=(-3)/5 is x=-0.64350…+2pin,x=pi+0.64350…+2pin

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sin(x)=(-3)/5

sin (x) = \frac{- 3}{5}

x = - 0.64350 \dots + 2 πn, x = π + 0.64350 \dots + 2 πn

Solution steps

sin (x) = \frac{- 3}{5}

Apply the fraction rule:

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

sin (x) = - \frac{3}{5}

Apply trig inverse properties

x = arcsin (- \frac{3}{5}) + 2 πn, x = π + arcsin (\frac{3}{5}) + 2 πn

Show solutions in decimal form

x = - 0.64350 \dots + 2 πn, x = π + 0.64350 \dots + 2 πn

3 cos^{2} (a) + sin^{2} (a) = 2

2 cos (6 x) + 3 = 0

2 = 2 sin (3 θ)

sin (\frac{π}{3} - x) = \frac{1}{2}

sin (x) = \frac{2}{3}

What is the general solution for sin(x)=(-3)/5 ?
The general solution for sin(x)=(-3)/5 is x=-0.64350…+2pin,x=pi+0.64350…+2pin