Find the Value Using the Unit Circle cos(315)

Problem

cos(315)

Solution

1. Identify the quadrant of the angle 315 Since 270<315<360 the angle lies in Quadrant IV.

2. Determine the reference angle θ′ For an angle in Quadrant IV, the reference angle is calculated as 360−θ

θ′=360−315

θ′=45

3. Recall the cosine value for the reference angle 45 from the unit circle.

cos(45)=√(,2)/2

4. Determine the sign of the cosine function in Quadrant IV. In the unit circle, cos(θ) corresponds to the xcoordinate. In Quadrant IV, xcoordinates are positive.

cos(315)>0

5. Combine the sign and the reference angle value to find the final result.

cos(315)=cos(45)

Final Answer

cos(315)=√(,2)/2

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