arcsin(x)=1/2 — step-by-step solution

1) Let's solve in

ℝ

\arcsin (x) = \frac{1}{2}

\arcsin

takes its values in

[- \frac{π}{2}, \frac{π}{2}]

, which contains

\frac{1}{2}

\arcsin (x) = \frac{1}{2}

is equivalent to

x = \sin (\frac{1}{2})

Candidates, pending the domain check:

x = \sin (\frac{1}{2})

2) Let's find the domain of

\arcsin (x) = \frac{1}{2}

For the expression

\arcsin (x)

to exist, you must check:

| x | \leq 1

| A | \leq B

is equivalent to

- B \leq A \leq B

-1 \leq x \leq 1

Domain constraints:

x \in [-1, 1]

▶Solution:

x = \sin (\frac{1}{2})

3) The numeric value of:

x = \sin (\frac{1}{2})

is:

x = \sin (0.5)

ⓘ The sine is the y-coordinate (vertical axis) of the point reached on the unit circle after a rotation of

0.5

radians from the horizontal axis pointing to the right

▷

x = \approx 0.4794