Find the Exact Value cos(495)

Problem

cos(495)

Solution

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

θ=495−360=135

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

3. Determine the sign of the cosine function in Quadrant II. In this quadrant, cosine values are negative.

4. Calculate the reference angle by subtracting the angle from 180

(θ_ref)=180−135=45

5. Apply the exact value for cos(45) which is √(,2)/2 and attach the negative sign determined in step 3.

cos(495)=−cos(45)=−√(,2)/2

Final Answer

cos(495)=−√(,2)/2

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