What is the general solution for sin(x)= 4/5 ,0<= x<2pi ?

The general solution for sin(x)= 4/5 ,0<= x<2pi is x=0.92729…,x=pi-0.92729…

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sin(x)= 4/5 ,0<= x<2pi

sin (x) = \frac{4}{5}, 0 \leq x < 2 π

x = 0.92729 \dots, x = π - 0.92729 \dots

Solution steps

sin (x) = \frac{4}{5}, 0 \leq x < 2 π

Apply trig inverse properties

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

Solutions for the range

0 \leq x < 2 π

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

Show solutions in decimal form

x = 0.92729 \dots, x = π - 0.92729 \dots

7 sin^{2} (θ) - 5 sin (θ) = 2

sec (2 x) = - (\frac{2}{3})

\frac{e ^{- l n (- \frac{s i n ( θ )}{c o s ( θ )})}}{2} \cdot sin (θ) = 0

7 sin (2 x) + 12 sin (x) = 0

x, cos (x) = cos (2 x)

What is the general solution for sin(x)= 4/5 ,0<= x<2pi ?
The general solution for sin(x)= 4/5 ,0<= x<2pi is x=0.92729…,x=pi-0.92729…