What is the value of sin
4
7π
?
- A2
3
- B3
2
- C−
2
1
- D−
3
2
Solution & Step-by-step Explanation
The given expression is sin
4
7π
.
We can rewrite the angle
4
7π
as:
4
7π
=2π−
4
π
Using the trigonometric identity sin(2π−θ)=−sinθ:
sin(2π−
4
π
)=−sin(
4
π
)
Since sin
4
π
=
2
1
:
sin
4
7π
=−
2
1
4
7π
.
We can rewrite the angle
4
7π
as:
4
7π
=2π−
4
π
Using the trigonometric identity sin(2π−θ)=−sinθ:
sin(2π−
4
π
)=−sin(
4
π
)
Since sin
4
π
=
2
1
:
sin
4
7π
=−
2
1