What is the value of sin(
3
5π
)?
- A2
3
- B\frac{2}{\sqrt{3}}
- C\frac{1}{\sqrt{3}}
- D−
2
3
Solution & Step-by-step Explanation
We need to evaluate sin(
3
5π
).
The angle
3
5π
can be rewritten as:
3
5π
=2π−
3
π
Using the trigonometric identity sin(2π−θ)=−sinθ (since the angle lies in the fourth quadrant where sine is negative):
sin(2π−
3
π
)=−sin(
3
π
)
We know that sin(
3
π
)=
2
3
. Therefore:
sin(
3
5π
)=−
2
3
3
5π
).
The angle
3
5π
can be rewritten as:
3
5π
=2π−
3
π
Using the trigonometric identity sin(2π−θ)=−sinθ (since the angle lies in the fourth quadrant where sine is negative):
sin(2π−
3
π
)=−sin(
3
π
)
We know that sin(
3
π
)=
2
3
. Therefore:
sin(
3
5π
)=−
2
3