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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