If sin(−
3
4π
)=x, then the value of x is
- A-2
- B−2/
3
- C3
/2 - D2
Solution & Step-by-step Explanation
We know that sin(−θ)=−sinθ.
x=sin(−
3
4π
)=−sin(
3
4π
)
Now express
3
4π
as π+
3
π
:
sin(π+
3
π
)=−sin(
3
π
)
Therefore:
x=−(−sin(
3
π
))=sin(
3
π
)
Since sin(
3
π
)=
2
3
:
x=
2
3
x=sin(−
3
4π
)=−sin(
3
4π
)
Now express
3
4π
as π+
3
π
:
sin(π+
3
π
)=−sin(
3
π
)
Therefore:
x=−(−sin(
3
π
))=sin(
3
π
)
Since sin(
3
π
)=
2
3
:
x=
2
3