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Determinant of Matrix Involving trig Functions

  1. Oct 5, 2012 #1
    1. The problem statement, all variables and given/known data

    Find the determinant of the matrix {{cos 25°, sin° 65}, {sin 120°, cos 390°}} (sorry, can't latex). {cos 25°, sin° 65} is first row and {sin 120°, cos 390°} is the second one.

    2. Relevant equations

    cos(a + b) = (cos a)(cos b) - (sin a) (sin b)

    3. The attempt at a solution

    I know you can just plug the values in a calculator, but apparently you can solve it by using some trig identities. I also though about using some property of rotation matrices but couldn't find any that fit the problem. Anyway, this is as far as I got:

    cos (a + b) = (cos 25°)(cos 390°) - (sin 65°) (sin 120°)
     
  2. jcsd
  3. Oct 5, 2012 #2
    Convert sin(65) into cos(something), rewrite sin(120) as sin(90+30), you can still do one more thing, cos(360+x)=cos(x). Can you start from here?
     
  4. Oct 5, 2012 #3
    Yeah, thanks! I was so caught up thinking on how to simplify the expression I forgot I could just keep on expanding it!
     
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