Simplify cos(495)

Problem

cos(495^∘)

Solution

1. Find the coterminal angle by subtracting 360^∘ from the given angle to bring it within the standard range of 0^∘ to 360^∘

495^∘−360^∘=135^∘

2. Identify the quadrant for 135^∘ Since 90^∘<135^∘<180^∘ the angle lies in Quadrant II.

3. Determine the reference angle for an angle in Quadrant II by subtracting the angle from 180^∘

180^∘−135^∘=45^∘

4. Apply the sign rule for cosine in Quadrant II. Since cosine is negative in the second quadrant, cos(135^∘)=−cos(45^∘)

5. Evaluate the cosine of the reference angle using known trigonometric values.

cos(45^∘)=√(,2)/2

Final Answer

cos(495^∘)=−√(,2)/2

Want more problems? Check here!