Find the principal solution of √3secx+2=0
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Step-by-step explanation:
√
3
sec
(
x
)
+
2
=
0
Subtract
2
from both sides of the equation.
√
3
sec
(
x
)
=
−
2
Divide each term by
√
3
and simplify.
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sec
(
x
)
=
−
2
√
3
3
Take the inverse secant of both sides of the equation to extract
x
from inside the secant.
x
=
arcsec
(
−
2
√
3
3
)
The exact value of
arcsec
(
−
2
√
3
3
)
is
5
π
6
.
x
=
5
π
6
The secant function is negative in the second and third quadrants. To find the second solution, subtract the reference angle from
2
π
to find the solution in the third quadrant.
x
=
2
π
−
5
π
6
Simplify
2
π
−
5
π
6
.
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