Find the Exact Value cos(315)

Problem

cos(315)

Solution

1. Identify the angle's position on the unit circle. The angle 315 is located in the fourth quadrant (270<315<360.

2. Determine the reference angle. The reference angle (θ_r*e*ƒ) for an angle in the fourth quadrant is calculated by subtracting the angle from 360

(θ_r*e*ƒ)=360−315

(θ_r*e*ƒ)=45

3. Apply the cosine sign rule for the fourth quadrant. In the fourth quadrant, the cosine function is positive.

cos(315)=cos(45)

4. Evaluate the exact value using the unit circle or special right triangles. The cosine of 45 is √(,2)/2

cos(45)=√(,2)/2

Final Answer

cos(315)=√(,2)/2

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