What is the general solution for arcsin(x)=0 ?

The general solution for arcsin(x)=0 is x=0

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arcsin(x)=0

arcsin (x) = 0

x = 0

Solution steps

arcsin (x) = 0

Apply trig inverse properties

arcsin (x) = 0

arcsin (x) = a \Rightarrow x = sin (a)

x = sin (0)

sin (0) = 0

sin (0)

Use the following trivial identity:

sin (0) = 0

sin (0)

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 0

= 0

x = 0

x = 0

tan (x) = 1.5

tan (3 x) = - 3

1 = cos (x)

(cot (θ) - 1) (2 sin (θ) + 1) = 0

sin (θ) = \frac{4}{7}

What is the general solution for arcsin(x)=0 ?
The general solution for arcsin(x)=0 is x=0