Find the Exact Value sin(-(11pi)/4)

Problem

sin(−(11*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]

(−11*π)/4+2*π=(−11*π)/4+(8*π)/4=(−3*π)/4

(−3*π)/4+2*π=(−3*π)/4+(8*π)/4=(5*π)/4

2. Identify the quadrant for the angle (5*π)/4 Since π<(5*π)/4<(3*π)/2 the angle lies in Quadrant III.

3. Determine the sign of the sine function in Quadrant III. In this quadrant, the sine value is negative.

4. Calculate the reference angle (θ_R) for (5*π)/4

(θ_R)=(5*π)/4−π=π/4

5. Evaluate the sine of the reference angle and apply the negative sign.

sin(π/4)=√(,2)/2

sin((5*π)/4)=−√(,2)/2

Final Answer

sin(−(11*π)/4)=−√(,2)/2

Want more problems? Check here!