What is the general solution for sin(α)= 3/5 ,0<a< pi/2 ?

The general solution for sin(α)= 3/5 ,0<a< pi/2 is α=0.64350…

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sin(α)= 3/5 ,0<a< pi/2

sin (α) = \frac{3}{5}, 0 < a < \frac{π}{2}

α = 0.64350 \dots

Degrees

α = 36.86989 \dots^{\circ}

Solution steps

sin (α) = \frac{3}{5}, 0 < a < \frac{π}{2}

Apply trig inverse properties

sin (α) = \frac{3}{5}

General solutions for

sin (α) = \frac{3}{5}

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

α = arcsin (\frac{3}{5}) + 2 πn, α = π - arcsin (\frac{3}{5}) + 2 πn

α = arcsin (\frac{3}{5}) + 2 πn, α = π - arcsin (\frac{3}{5}) + 2 πn

Solutions for the range

0 < a < \frac{π}{2}

α = arcsin (\frac{3}{5})

Show solutions in decimal form

α = 0.64350 \dots

- \frac{15 ( 0.5 cos ( x ) - sin ( x ) )}{( 0.5 sin ( x ) + cos ( x ) ) ^{2}} = 0

x, 0.33 = sin (209.42 x)

- 2 + tan (θ) = - 1

sin^{2} (x) + cos^{2} (\frac{2}{5}) = 1

3 \cdot cos (4 θ) = 0

What is the general solution for sin(α)= 3/5 ,0<a< pi/2 ?
The general solution for sin(α)= 3/5 ,0<a< pi/2 is α=0.64350…