# What exactly is a "Double Angle"?

• Feb 27th 2011, 07:01 PM
Slappydappy
What exactly is a "Double Angle"?
I had a question about Trig. Double angle formulas….why is it called “double angle”? For instance, say we have Cos 2x. Does this mean we are multiplying the value of the angle by 2 and then taking the Cosine of it? So 150 degrees would 300 degrees? And then we take the Cosine of it? I understand how to calculate these using the formulas, I just don't understand what a double angle is (visually I guess).

Also, why does Cosine have 3 ways of calculating a double angle and Sine only has 1?
• Feb 27th 2011, 07:22 PM
topsquark
Quote:

Originally Posted by Slappydappy
Does this mean we are multiplying the value of the angle by 2 and then taking the Cosine of it?

That's it exactly.

-Dan
• Feb 27th 2011, 07:24 PM
topsquark
Quote:

Originally Posted by Slappydappy
Also, why does Cosine have 3 ways of calculating a double angle and Sine only has 1?

It is simply that the form for sin(2x) does not include the square of sine or cosine. We have three different forms for cosine squared becasue we can use the identity $sin^2(x) + cos^2(x) = 1$ in various ways with it.

-Dan
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