cos 2x
The term “cos 2x” represents the cosine of twice the value of angle x
The term “cos 2x” represents the cosine of twice the value of angle x. To understand this, we need to recall the double-angle identity for cosine.
The double-angle identity for cosine states that cos 2x = cos^2 x – sin^2 x.
You can also express this identity in terms of cos alone by using the identity sin^2 x = 1 – cos^2 x.
Therefore, cos 2x = cos^2 x – (1 – cos^2 x) or cos 2x = 2cos^2 x – 1.
In other words, when we know the value of angle x, we can use the double-angle identity to find the value of cos 2x.
For example, let’s say x = 30 degrees. We can use this information to find the value of cos 2x.
cos 2x = cos 2(30) = cos 60
Now, we know that cos 60 degrees is equal to 0.5 (you can find this value in a trigonometric table or use a calculator). Therefore, cos 2x = 0.5.
So, in this particular case, when x is 30 degrees, cos 2x equals 0.5.
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