if sin x = root 3/2 , find x
Answers
Step-by-step explanation:
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Precalculus Examples
Popular Problems Precalculus Solve for x sin(x)=( square root of 3)/2
sin
(
x
)
=
√
3
2
Take the inverse sine of both sides of the equation to extract
x
from inside the sine.
x
=
arcsin
(
√
3
2
)
The exact value of
arcsin
(
√
3
2
)
is
π
3
.
x
=
π
3
The sine function is positive in the first and second quadrants. To find the second solution, subtract the reference angle from
π
to find the solution in the second quadrant.
x
=
π
−
π
3
Simplify
π
−
π
3
.
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x
=
2
π
3
Find the period.
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2
π
The period of the
sin
(
x
)
function is
2
π
so values will repeat every
2
π
radians in both directions.
x
=
π
3
+
2
π
n
,
2
π
3
+
2
π
n
, for any integer
n
Step-by-step explanation:
sin(x)=(√32).
So , what is the principal solution ?
We know that sin(60°)=(√32).
So , the principal solution is x = 60° .
x = 60° can be represented as x=π3radians.
Thus the principal solution is x=π3radians.
Now the general solution for
sin x = y= sin z is z=nπ+(−1)nx.
Thus the general solution for
sin(x)=(√32) is
x=nπ+(−1)nπ3.