this is just a general trig question: We are going over Malus law in physics; the formula is this: S = s*cos^2(theta) My question is about the cosine squared term in the equation. does this simply mean take the cosine of a number and square it? in other words would this be the same thing as [cos(theta)]^2
Indeed! It is an unfortunate notation that confuses a lot of students, but it won't ever go away. you have to live with it.
I simply tell my students that once upon a time, they wrote it as (sinx)^2, but lazy students kept leaving off the parenthesis and wrote sinx^2, sometimes meaning to take the sine of x, then square that answer; other times meaning to square the x first, then take the sine. To eliminate confusion, when they want the sin value to be squared, they put the squared symbol right next to sin [tex]sin^{2}x[/tex] So, to shorten [tex](sinx)^2[/tex] write [tex]sin^{2}x[/tex] and to shorten [tex]sin(x^2)[/tex] write [tex]sinx^2[/tex] (although some people prefer those parenthesis are left in the latter case.)