Find the Exact Value sin(-(13pi)/4)

Problem

sin(−(13*π)/4)

Solution

1. Find a coterminal angle by adding multiples of 2*π to the angle until it falls within the interval [0,2*π)

(−13*π)/4+2*π=(−13*π)/4+(8*π)/4=(−5*π)/4

(−5*π)/4+2*π=(−5*π)/4+(8*π)/4=(3*π)/4

2. Identify the quadrant for the angle (3*π)/4 Since π/2<(3*π)/4<π the angle is in Quadrant II.

3. Determine the reference angle for (3*π)/4 in Quadrant II.

π−(3*π)/4=π/4

4. Apply the sine sign rule for Quadrant II. In Quadrant II, the sine function is positive.

sin((3*π)/4)=sin(π/4)

5. Evaluate the exact value of the sine of the reference angle.

sin(π/4)=√(,2)/2

Final Answer

sin(−(13*π)/4)=√(,2)/2

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