- #1
justine411
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Homework Statement
(cos2x)^2
Homework Equations
The Attempt at a Solution
I'm not sure if it is cos^2(2x) or cos^2(4x) or what. Should I use an identity to simplify it to make it easier to solve? Please help! :)
HallsofIvy said:In what sense is (cos(2x))2 a "problem"? What do you want to do with it?
I will say that (cos(2x))2 means: First calculate 2x, then find cosine of that and finally square that result. Notice that it is still 2x, not 4x. The fact that 2 is outside the parentheses means that it only applies to the final result.
Rhythmer said:Doesn't (cos(2x))2 = cos2(2x)2 = cos2(4x2) ?
The identity of (cos(2x))^2 is equal to 1/2(1+cos(4x)), which can also be written as 1/2 + 1/2cos(4x).
To simplify (cos(2x))^2, you can use the double angle formula for cosine: cos(2x) = 1-2sin^2(x). This can be substituted into the original equation to get (1-2sin^2(x))^2, which can then be expanded and simplified further.
No, (cos(2x))^2 cannot be negative. The square of any real number will always result in a positive number, including the cosine function.
Yes, (cos(2x))^2 can be greater than 1. Since the cosine function can take on values between -1 and 1, squaring it will result in a value greater than 1 if the original value was greater than 1 or less than -1.
The period of (cos(2x))^2 is the same as the period of the cosine function, which is 2π. This means that the graph of (cos(2x))^2 will repeat itself every 2π units on the x-axis.