Understanding the Double-Angle Identity for Cosine and How to Find Cos 2x given an Angle x

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.

More Answers:
Understanding the Cosine Function | Exploring cos(-x) and its Relationship with cos(x) on the Unit Circle
Understanding the Two Interpretations of sin^2x and the Double-Angle Formula
Understanding the Relationship | sin(-x) is the Negative of sin(x)

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