Sin inverse {cos (Sin inverse root 3 by 2)}
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Answer:
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Explanation:
Consider an equilateral triangle with sides of length
2
, bisected to form two right angled triangles:
enter image source here
Remembering that
sin
=
opposite
hypotenuse
, we can see that:
sin
(
π
3
)
=
√
3
2
Since
√
3
2
>
0
and
π
3
is in Q1, we can deduce:
sin
−
1
(
√
3
2
)
=
π
3
From the same diagram, remembering
cos
=
adjacent
hypotenuse
, we can see that:
cos
(
π
3
)
=
1
2
So:
cos
(
sin
−
1
(
√
3
2
)
)
=
cos
(
π
3
)
=
1
2
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