If tan(−
3
5π
)=x, then the value of x is
- A3
- B1
- C−1/2
- D3
/2
Solution & Step-by-step Explanation
We need to evaluate x=tan(−
3
5π
).
Using the identity tan(−θ)=−tanθ:
x=−tan(
3
5π
)
Now rewrite
3
5π
in terms of a multiple of 2π or π:
3
5π
=2π−
3
π
Substitute this back into the expression:
x=−tan(2π−
3
π
)
Since tan(2π−θ)=−tanθ:
x=−(−tan(
3
π
))=tan(
3
π
)
We know that tan(
3
π
)=
3
. Thus, x=
3
.
3
5π
).
Using the identity tan(−θ)=−tanθ:
x=−tan(
3
5π
)
Now rewrite
3
5π
in terms of a multiple of 2π or π:
3
5π
=2π−
3
π
Substitute this back into the expression:
x=−tan(2π−
3
π
)
Since tan(2π−θ)=−tanθ:
x=−(−tan(
3
π
))=tan(
3
π
)
We know that tan(
3
π
)=
3
. Thus, x=
3
.