If cot(−
4
5π
)=x, then the value of x is:
- A3
- B1
- C−1
- D−
2
1
Solution & Step-by-step Explanation
We know that cot(−θ)=−cotθ.
Therefore:
cot(−
4
5π
)=−cot(
4
5π
)
Now, express
4
5π
in terms of basic angles:
4
5π
=π+
4
π
We know that cot(π+θ)=cotθ because cotangent is positive in the third quadrant:
cot(π+
4
π
)=cot(
4
π
)=1
Substituting this back:
x=−cot(
4
5π
)=−(1)=−1
Therefore:
cot(−
4
5π
)=−cot(
4
5π
)
Now, express
4
5π
in terms of basic angles:
4
5π
=π+
4
π
We know that cot(π+θ)=cotθ because cotangent is positive in the third quadrant:
cot(π+
4
π
)=cot(
4
π
)=1
Substituting this back:
x=−cot(
4
5π
)=−(1)=−1