What is the general solution for sin(x)=-4/5 ?

The general solution for sin(x)=-4/5 is x=-0.92729…+2pin,x=pi+0.92729…+2pin

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sin(x)=-4/5

sin (x) = - \frac{4}{5}

x = - 0.92729 \dots + 2 πn, x = π + 0.92729 \dots + 2 πn

Degrees

x = - 53.13010 \dots^{\circ} + 36 0^{\circ} n, x = 233.13010 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) = - \frac{4}{5}

Apply trig inverse properties

sin (x) = - \frac{4}{5}

General solutions for

sin (x) = - \frac{4}{5}

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

x = arcsin (- \frac{4}{5}) + 2 πn, x = π + arcsin (\frac{4}{5}) + 2 πn

x = arcsin (- \frac{4}{5}) + 2 πn, x = π + arcsin (\frac{4}{5}) + 2 πn

Show solutions in decimal form

x = - 0.92729 \dots + 2 πn, x = π + 0.92729 \dots + 2 πn

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

(tan (x) - 1) (cos (x) + 1) = 0

cos (2 x) = \frac{- 1}{2}

cos (2 x - \frac{π}{6}) = \frac{3}{2}

12 cos^{2} (θ) = 9

What is the general solution for sin(x)=-4/5 ?
The general solution for sin(x)=-4/5 is x=-0.92729…+2pin,x=pi+0.92729…+2pin