Step 1: Determine in which quadrant the given angle lies.

              GIVEN: \cos 495\degree

                           \theta = 495

              The given angle is more then 360\degree

              So, 495\degree-360\degree=135\degree

                  135\degree  is between 90\degree and 180\degree  it will lie in Quadrant II.

Step 2: Calculate the exact value of the ratio.


              Find the reference angle. Since we are in Quadrant II

            So, \cos(135\degree)=\cos(180\degree\ -\ 45\degree)=-\ \cos45\degree  

                \cos45\degree=\ -\frac{1}{\sqrt{2}}

Step 3: Reason for the negative sign of the value

            In Quadrant II, the \cos \theta is negative. only sine is positive



          Therefore, the exact value \cos 45 = - \frac{1}{\sqrt{2}}