What is the general solution for sin(2x)=-4/5 ?

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

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sin(2x)=-4/5

sin (2 x) = - \frac{4}{5}

x = - \frac{0.92729 \dots}{2} + πn, x = \frac{π}{2} + \frac{0.92729 \dots}{2} + πn

Solution steps

sin (2 x) = - \frac{4}{5}

Apply trig inverse properties

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

Solve

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

Solve

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

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

Show solutions in decimal form

x = - \frac{0.92729 \dots}{2} + πn, x = \frac{π}{2} + \frac{0.92729 \dots}{2} + πn

5 sin (x) - 2 = 0

5 cos^{2} (x) - 2 cos (x) - 3 = sin^{2} (x)

10 cos (θ) = 6

- cos (x) = cos (- x)

5 sin (θ) + 1 = 3 sin (θ)

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