Find the Exact Value cos(315 degrees )

Problem

cos(315)

Solution

1. Identify the reference angle by finding the difference between 315 and the nearest x-axis angle, which is 360

(θ_ref)=360−315

(θ_ref)=45

2. Determine the quadrant in which 315 lies. Since 270<315<360 the angle is in Quadrant IV.

3. Determine the sign of the cosine function in Quadrant IV. In this quadrant, the x-coordinates are positive, so cos(θ) is positive.

cos(315)=cos(45)

4. Evaluate the exact value of the cosine of the reference angle using the unit circle or special right triangles.

cos(45)=√(,2)/2

Final Answer

cos(315)=√(,2)/2

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