If sin(−
3
5π
)=x, then the value of x is:
- A−
3
/2 - B3
/2 - C−2
- D−2/
3
Solution & Step-by-step Explanation
Using the identity sin(−θ)=−sinθ:
sin(−
3
5π
)=−sin(
3
5π
)
Now express
3
5π
in terms of 2π:
3
5π
=2π−
3
π
Using the identity sin(2π−θ)=−sinθ:
−sin(2π−
3
π
)=−(−sin
3
π
)=sin
3
π
We know that sin
3
π
=
2
3
.
Thus, x=
2
3
.
sin(−
3
5π
)=−sin(
3
5π
)
Now express
3
5π
in terms of 2π:
3
5π
=2π−
3
π
Using the identity sin(2π−θ)=−sinθ:
−sin(2π−
3
π
)=−(−sin
3
π
)=sin
3
π
We know that sin
3
π
=
2
3
.
Thus, x=
2
3
.