# Thread: Double angles and trig ratios

1. ## Double angles and trig ratios

Hi,

I hope someone can help. I'm trying to rewrite the trig ratio cos3x to fit within a double angle formula. These are the steps which I have followed: https://www.algebra.com/algebra/home...on.182274.html

While I understand the steps listed in the link that I pasted above, it does not provide me with the solution that I'm looking for. The solution for this problem according to my textbook is 2cos^2(1.5x-1).

Any ideas on how to solve this problem in order for it to match up with the textbook's solution?

Sincerely,
Olivia

2. ## Re: Double angles and trig ratios

Why would you have 1.5x - 1?

3. ## Re: Double angles and trig ratios

Originally Posted by otownsend
... The solution for this problem according to my textbook is 2cos^2(1.5x-1)
You made an error in typing the expression ... should be $2\cos^2(1.5x)-1$

Note the double angle identity for cosine ...

$\cos(2\theta) = 2\cos^2(\theta)-1$

now, let $\theta = \dfrac{3x}{2}$ ...

4. ## Re: Double angles and trig ratios

Okay so you're saying that is one way to solve this is the way which you are describing above, and another way is this https://www.algebra.com/algebra/home...on.182274.html?

If that is the case then I find it odd that both solutions (solution 1 - 2cos^2(1.5x)-1 and solution 2 - 4cos^3-3cosx look entirely different when I graph them... why is this?

6. ## Re: Double angles and trig ratios

If that is the case then I find it odd that both solutions (solution 1 - 2cos^2(1.5x)-1 and solution 2 - 4cos^3-3cosx look entirely different when I graph them... why is this?
Maybe you didn't enter each expression correctly into the grapher.

attached are three graphs, all the same ...

$\color{blue}{y = \cos(3x)}$

$y = 2\cos^2(1.5x)-1$

$\color{red}{y=4\cos^3{x}-3\cos{x}}$

7. ## Re: Double angles and trig ratios

The reason why I got different graphs was because Desmos doesn't allow any trig ratio with a power larger than 2.

But now after looking at that link SlipEternal posted, and the graphs skeeter created I definetely see that 4cos^3-3cosx and 2cos^2(1.5x)-1 are the same.