If cot(−
3
4π
)=x, then the value of x is:
- A-1
- B-\frac{1}{\sqrt{3}}
- C\sqrt{3}
- D1
Solution & Step-by-step Explanation
Using trigonometric identity properties:
cot(−θ)=−cot(θ)
Thus:
x=cot(−
3
4π
)=−cot(
3
4π
)
We can rewrite
3
4π
as π+
3
π
:
cot(π+
3
π
)=cot(
3
π
)
Since cot(
3
π
)=
3
1
:
x=−(
3
1
)=−
3
1
cot(−θ)=−cot(θ)
Thus:
x=cot(−
3
4π
)=−cot(
3
4π
)
We can rewrite
3
4π
as π+
3
π
:
cot(π+
3
π
)=cot(
3
π
)
Since cot(
3
π
)=
3
1
:
x=−(
3
1
)=−
3
1