Determinant of Matrix Involving trig Functions

AI Thread Summary
The discussion focuses on finding the determinant of a matrix involving trigonometric functions. The matrix in question is composed of cosine and sine values at specific angles. Participants suggest using trigonometric identities and properties, such as the cosine of angle sums, to simplify the expressions. There is a mention of using rotation matrix properties, although no specific property is identified. The conversation highlights the importance of expanding expressions rather than solely simplifying them.
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Homework Statement



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.

Homework Equations



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

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°)
 
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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?
 
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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