If sec(−
4
7π
)=x, then the value of x is:
- A2
- B−
2
- C−
3
1
- D-1
Solution & Step-by-step Explanation
We know that sec(−θ)=secθ. Therefore:
sec(−
4
7π
)=sec(
4
7π
)
Now, we can express
4
7π
as 2π−
4
π
:
sec(
4
7π
)=sec(2π−
4
π
)
Since sec(2π−θ)=secθ (as it lies in the fourth quadrant where secant is positive):
sec(2π−
4
π
)=sec(
4
π
)
We know that sec(
4
π
)=
2
.
Therefore, x=
2
.
sec(−
4
7π
)=sec(
4
7π
)
Now, we can express
4
7π
as 2π−
4
π
:
sec(
4
7π
)=sec(2π−
4
π
)
Since sec(2π−θ)=secθ (as it lies in the fourth quadrant where secant is positive):
sec(2π−
4
π
)=sec(
4
π
)
We know that sec(
4
π
)=
2
.
Therefore, x=
2
.