What is the general solution for arcsin(4/5)=sin(x) ?

The general solution for arcsin(4/5)=sin(x) is x=1.18712…+2pin,x=pi-1.18712…+2pin

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arcsin(4/5)=sin(x)

arcsin (\frac{4}{5}) = sin (x)

x = 1.18712 \dots + 2 πn, x = π - 1.18712 \dots + 2 πn

Solution steps

arcsin (\frac{4}{5}) = sin (x)

Switch sides

sin (x) = arcsin (\frac{4}{5})

Apply trig inverse properties

sin (x) = arcsin (\frac{4}{5})

General solutions for

sin (x) = arcsin (\frac{4}{5})

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

x = arcsin (arcsin (\frac{4}{5})) + 2 πn, x = π - arcsin (arcsin (\frac{4}{5})) + 2 πn

x = arcsin (arcsin (\frac{4}{5})) + 2 πn, x = π - arcsin (arcsin (\frac{4}{5})) + 2 πn

Show solutions in decimal form

x = 1.18712 \dots + 2 πn, x = π - 1.18712 \dots + 2 πn

4 sin^{2} (x - 6 0^{\circ}) = 3

cos (a) = - \frac{4}{5}, 9 0^{\circ} < a < 18 0^{\circ}

3 cot^{2} (2 x - \frac{3 π}{2}) = 1

1.6 sin (θ) = 1.49

cos (x) = 0.695

What is the general solution for arcsin(4/5)=sin(x) ?
The general solution for arcsin(4/5)=sin(x) is x=1.18712…+2pin,x=pi-1.18712…+2pin