Find the Value Using the Unit Circle sin((5pi)/4)

Problem

sin((5*π)/4)

Solution

1. Identify the angle (5*π)/4 on the unit circle. This angle is located in the third quadrant because π<(5*π)/4<(3*π)/2

2. Determine the reference angle by subtracting π from the given angle.

Reference Angle=(5*π)/4−π=π/4

3. Recall the sine value for the reference angle π/4

sin(π/4)=√(,2)/2

4. Apply the sign for the third quadrant. In the third quadrant, both sine (ycoordinate) and cosine (xcoordinate) are negative.

sin((5*π)/4)=−√(,2)/2

Final Answer

sin((5*π)/4)=−√(,2)/2

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