What is the general solution for sin(a)= 5/9 ?

The general solution for sin(a)= 5/9 is a=0.58903…+2pin,a=pi-0.58903…+2pin

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sin(a)= 5/9

sin (a) = \frac{5}{9}

a = 0.58903 \dots + 2 πn, a = π - 0.58903 \dots + 2 πn

Degrees

a = 33.74898 \dots^{\circ} + 36 0^{\circ} n, a = 146.25101 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (a) = \frac{5}{9}

Apply trig inverse properties

sin (a) = \frac{5}{9}

General solutions for

sin (a) = \frac{5}{9}

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

a = arcsin (\frac{5}{9}) + 2 πn, a = π - arcsin (\frac{5}{9}) + 2 πn

a = arcsin (\frac{5}{9}) + 2 πn, a = π - arcsin (\frac{5}{9}) + 2 πn

Show solutions in decimal form

a = 0.58903 \dots + 2 πn, a = π - 0.58903 \dots + 2 πn

sin (x - 2 0^{\circ}) = \frac{1}{2}

tan^{2} (x) + 2 sec^{2} (x) = 3

sin (x) = 5 cos (x)

cos (5 x) - cos (x) = sin (5 x) - sin (x)

\frac{1}{4} = sin (x)

What is the general solution for sin(a)= 5/9 ?
The general solution for sin(a)= 5/9 is a=0.58903…+2pin,a=pi-0.58903…+2pin