## How to find answer of y = 0 using double angle formulas

Trigonometric ratios and functions, the unit circle, inverse trig functions, identities, trig graphs, etc.
Aaahhhh Fuuu.....
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### How to find answer of y = 0 using double angle formulas

This equation cos2theta = 1, the closest equation using cos2theta double angle formula is the cos^2x - sin^2x version. But it is not exact. Can anyone show me the steps on how to complete the equation? The answer of 0 = 2y^2 is the nearest to y = 0 that I can solve without completing using dividing by two then square rooting.

maggiemagnet
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### Re: How to find answer of y = 0 using double angle formulas

Aaahhhh Fuuu..... wrote:This equation cos2theta = 1, the closest equation using cos2theta double angle formula is the cos^2x - sin^2x version. But it is not exact. Can anyone show me the steps on how to complete the equation? The answer of 0 = 2y^2 is the nearest to y = 0 that I can solve without completing using dividing by two then square rooting.

Why not solve the equation as it is? You have cos(2@) = 1. For what values of 2@ is the cosine equal to 1? Then divide by 2 to find the values for @.

Aaahhhh Fuuu.....
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### Re: How to find answer of y = 0 using double angle formulas

"Throw yo' hands up!?"
Attach yourself to this aspect of the equation if I did not mention it: The problem is asking to convert from polar to rectangular. Looking over my question I see I did not mention this part.

maggiemagnet
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### Re: How to find answer of y = 0 using double angle formulas

Aaahhhh Fuuu..... wrote:"Throw yo' hands up!?"
Attach yourself to this aspect of the equation if I did not mention it: The problem is asking to convert from polar to rectangular. Looking over my question I see I did not mention this part.

I didn't know. Sorry. I didn't mean to offend you.

Aaahhhh Fuuu.....
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### Re: How to find answer of y = 0 using double angle formulas

The only thing I need some instruction for this problem of cos2theta = 1 using polar to rectangular form. The result shown in the book is y = 0 but without any methods just the answer is useless. Thank you for your sympathies

Martingale
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### Re: How to find answer of y = 0 using double angle formulas

Aaahhhh Fuuu..... wrote:The only thing I need some instruction for this problem of cos2theta = 1 using polar to rectangular form. The result shown in the book is y = 0 but without any methods just the answer is useless. Thank you for your sympathies

hmmmm...

well....we 'know' right....that

$x^2+y^2=r^2$

and

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

we also have $x=r\cos(\theta)$ and $y=r\sin(\theta)$ so $\left(x^2+y^2=r^2\right)$

thus

$\frac{x}{r}=\cos(\theta)$ and $\frac{y}{r}=\sin(\theta)$

sooooooo.....

$\cos(2\theta)=1$

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

... start replacing the above with what we know and the solution will follow...

Aaahhhh Fuuu.....
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### Re: How to find answer of y = 0 using double angle formulas

Thank you Martingale.