What is the general solution for sin(x)= 53/54 ?

The general solution for sin(x)= 53/54 is x=1.37804…+2pin,x=pi-1.37804…+2pin

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sin(x)= 53/54

sin (x) = \frac{53}{54}

x = 1.37804 \dots + 2 πn, x = π - 1.37804 \dots + 2 πn

Solution steps

sin (x) = \frac{53}{54}

Apply trig inverse properties

x = arcsin (\frac{53}{54}) + 2 πn, x = π - arcsin (\frac{53}{54}) + 2 πn

Show solutions in decimal form

x = 1.37804 \dots + 2 πn, x = π - 1.37804 \dots + 2 πn

2 sin^{2} (x) + sin (x) - 3 = 0

(2 cos (x) - 1) sin (x) = 0

u, x = 4 sin (u)

2 cos (θ) = 2, 0 \leq θ < 2 π

cosh (θ) = 4 - j

What is the general solution for sin(x)= 53/54 ?
The general solution for sin(x)= 53/54 is x=1.37804…+2pin,x=pi-1.37804…+2pin