Find the Exact Value sin((5pi)/3)

Problem

sin((5*π)/3)

Solution

1. Identify the quadrant of the angle (5*π)/3 Since (3*π)/2<(5*π)/3<2*π the angle lies in Quadrant IV.

2. Determine the sign of the sine function in Quadrant IV. In this quadrant, the ycoordinates are negative, so sin((5*π)/3) must be negative.

3. Calculate the reference angle θ′ For an angle in Quadrant IV, the reference angle is found by subtracting the angle from 2*π

θ′=2*π−(5*π)/3

θ′=(6*π)/3−(5*π)/3

θ′=π/3

4. Evaluate the sine of the reference angle. Using the unit circle or special triangles, we know the value for π/3

sin(π/3)=√(,3)/2

5. Apply the sign from step 2 to the value from step 4 to find the final result.

sin((5*π)/3)=−√(,3)/2

Final Answer

sin((5*π)/3)=−√(,3)/2

Want more problems? Check here!