As we know
cos
(
a
)
=
x
=
x
1
we can label the adjacent leg as
x
and the hypotenuse as
1
. The Pythagorean theorem then allows us to solve for the second leg as
√
1
−
x
2
.
With this, we can now find
sin
(
cos
−
1
(
x
)
)
as the quotient of the opposite leg and the hypotenuse.
sin
(
cos
−
1
(
x
)
)
=
sin
(
a
)
=
√
1
−
x
2
1
=
√
1
−
x
2