Find the Exact Value cos((3pi)/4)

Problem

cos((3*π)/4)

Solution

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

2. Determine the sign of the cosine function in Quadrant II. In this quadrant, the xcoordinates are negative, so cos(θ) is negative.

3. Calculate the reference angle θ′ The reference angle for an angle in Quadrant II is found using θ′=π−θ

θ′=π−(3*π)/4

θ′=π/4

4. Evaluate the cosine of the reference angle. The value of cos(π/4) is a standard trigonometric value.

cos(π/4)=√(,2)/2

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

cos((3*π)/4)=−√(,2)/2

Final Answer

cos((3*π)/4)=−√(,2)/2

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