1. ## trigonometry

You are using trigonometry very well in geometry. Iknow all the trig. formulas but I can only solve equations.
I also don't like memorizing anything. I would like to learn if I can find sin18 or sin36 without memorizing anything or without referring to a trigonometry table.

3. ## Re: trigonometry

That seems alot of word. An equation of fifth degree. I know: 22.5,30,90,180,67.5,60,45.
Butthey don't seem enough to calculate 36 degrees or 72 degrees.

4. ## Re: trigonometry

Originally Posted by kastamonu
That seems alot of word. An equation of fifth degree. I know: 22.5,30,90,180,67.5,60,45.
Butthey don't seem enough to calculate 36 degrees or 72 degrees.
... and after factoring out an $x$, it became a fourth degree equation quadratic in $x^2$ ... did you even follow the derivation?

Do you understand that $\dfrac{\pi}{5}$ and $36^\circ$ are the same angle?

5. ## Re: trigonometry

I don't know this multiple-angle formula. I am seeing it for the first time. I am not responsible from it. It is out of the school curriculum.

We just know cos(a+b),cos(2a),tan(a-b),sina+sinb,cosa+cosb.. etc....

6. ## Re: trigonometry

It is easy to derive. The triple angle formula is found by $\sin(3x) = \sin(2x +x)$. Use the sum of angles formula. Then, for the 5x angle formula, use the sum of angles formula for $\sin(3x+2x)$. Easy peasy.

many thanks.