cos(x+π/3)=-1. where -2π<x<2π find the value of x
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Answer:
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Trigonometry Examples
Popular Problems Trigonometry Solve for ? cos(x-pi/3)-1=0
cos
(
x
−
π
3
)
−
1
=
0
cos(x-π3)-1=0
Add
1
1 to both sides of the equation.
cos
(
x
−
π
3
)
=
1
cos(x-π3)=1
Take the inverse cosine of both sides of the equation to extract
x
x from inside the cosine.
x
−
π
3
=
arccos
(
1
)
x-π3=arccos(1)
The exact value of
arccos
(
1
)
arccos(1) is
0
0.
x
−
π
3
=
0
x-π3=0
Add
π
3
π3 to both sides of the equation.
x
=
π
3
x=π3
The cosine function is positive in the first and fourth quadrants. To find the second solution, subtract the reference angle from
2
π
2π to find the solution in the fourth quadrant.
x
−
π
3
=
2
π
−
0
x-π3=2π-0
Simplify the expression to find the second solution.
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x
=
π
3
x=π3
Find the period.
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2
π
2π
The period of the
cos
(
x
−
π
3
)
cos(x-π3) function is
2
π
2π so values will repeat every
2
π
2π radians in both directions.
x
=
π
3
+
2
π
n
x=π3+2πn, for any integer
n
n