Sin(5π/3)
To find the value of sin(5π/3), we can use the unit circle and the concept of reference angles
To find the value of sin(5π/3), we can use the unit circle and the concept of reference angles.
First, let’s determine the reference angle for 5π/3. The reference angle is the acute angle formed between the terminal side of the angle and the x-axis.
In this case, 5π/3 is a negative angle measured clockwise from the positive x-axis. To find the reference angle, we can subtract the angle measure from a full revolution or 2π.
Reference angle = 2π – 5π/3
= 6π/3 – 5π/3
= π/3
Now that we have determined the reference angle to be π/3, we can use the properties of the unit circle to find the value of sin(π/3).
On the unit circle, the reference angle π/3 corresponds to the point (cos(π/3), sin(π/3)).
The value of cos(π/3) is 1/2 and sin(π/3) is √3/2.
Therefore, sin(5π/3) = sin(π/3) = √3/2.
So the answer is √3/2.
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