Simplify cos(315)

Problem

cos(315)

Solution

1. Identify the angle's position on the unit circle. The angle 315 is in the fourth quadrant.

2. Find the reference angle. Since 315 is in the fourth quadrant, the reference angle is calculated as 360−315=45

3. Determine the sign of the cosine function. In the fourth quadrant, the cosine of an angle is positive.

4. Apply the reference angle identity. The value of cos(315) is equal to cos(45)

5. Evaluate the trigonometric value. Using the standard values for special angles, cos(45)=√(,2)/2

Final Answer

cos(315)=√(,2)/2

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