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

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