What is the general solution for sin(a)= 20/30 ?

The general solution for sin(a)= 20/30 is a=0.72972…+2pin,a=pi-0.72972…+2pin

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sin(a)= 20/30

sin (a) = \frac{20}{30}

a = 0.72972 \dots + 2 πn, a = π - 0.72972 \dots + 2 πn

Degrees

a = 41.81031 \dots^{\circ} + 36 0^{\circ} n, a = 138.18968 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (a) = \frac{20}{30}

Cancel the common factor:

10

sin (a) = \frac{2}{3}

Apply trig inverse properties

sin (a) = \frac{2}{3}

General solutions for

sin (a) = \frac{2}{3}

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

a = arcsin (\frac{2}{3}) + 2 πn, a = π - arcsin (\frac{2}{3}) + 2 πn

a = arcsin (\frac{2}{3}) + 2 πn, a = π - arcsin (\frac{2}{3}) + 2 πn

Show solutions in decimal form

a = 0.72972 \dots + 2 πn, a = π - 0.72972 \dots + 2 πn

sin (θ + 1 5^{\circ}) = \frac{2}{3}

θ, 2 sin (θ) - 1 = 0

- 10 sin (x) = - 52

\frac{sin ( 11 5 ^{\circ} )}{20} = \frac{sin ( b )}{11}

y, \frac{sin ( 7 y )}{7} = \frac{cos ( 2 x )}{2} + \frac{1}{2}

What is the general solution for sin(a)= 20/30 ?
The general solution for sin(a)= 20/30 is a=0.72972…+2pin,a=pi-0.72972…+2pin