What is the general solution for sin(a)= 2/5 ?

The general solution for sin(a)= 2/5 is a=0.41151…+2pin,a=pi-0.41151…+2pin

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sin(a)= 2/5

sin (a) = \frac{2}{5}

a = 0.41151 \dots + 2 πn, a = π - 0.41151 \dots + 2 πn

Degrees

a = 23.57817 \dots^{\circ} + 36 0^{\circ} n, a = 156.42182 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (a) = \frac{2}{5}

Apply trig inverse properties

sin (a) = \frac{2}{5}

General solutions for

sin (a) = \frac{2}{5}

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

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

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

Show solutions in decimal form

a = 0.41151 \dots + 2 πn, a = π - 0.41151 \dots + 2 πn

cos^{2} (θ) - cos (θ) - 1 = 0

3 cot^{2} (x) - 4 csc (x) = 1

\frac{18 cos ( 2 θ ) + 27 cos ( θ )}{2} = 0

cos (x) = sin (2 x) + cos (3 x)

tan (x) sec (x) - 2 tan (x) = 0

What is the general solution for sin(a)= 2/5 ?
The general solution for sin(a)= 2/5 is a=0.41151…+2pin,a=pi-0.41151…+2pin