Simplify cos((11pi)/4)

Problem

cos((11*π)/4)

Solution

1. Identify the angle and find its coterminal equivalent within the standard interval [0,2*π] by subtracting multiples of 2*π

(11*π)/4−2*π=(11*π)/4−(8*π)/4

(11*π)/4−(8*π)/4=(3*π)/4

2. Determine the quadrant of the angle (3*π)/4 Since π/2<(3*π)/4<π the angle lies in Quadrant II.

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

π−(3*π)/4=π/4

4. Apply the cosine sign for Quadrant II. In Quadrant II, cosine values are negative.

cos((3*π)/4)=−cos(π/4)

5. Evaluate the trigonometric value using the known value for cos(π/4)

cos(π/4)=√(,2)/2

cos((3*π)/4)=−√(,2)/2

Final Answer

cos((11*π)/4)=−√(,2)/2

Want more problems? Check here!