Sin36=? without using calculator

2. Originally Posted by mialkan
Sin36=?
You use a calculator.

And hey ..... what happens if you google

sin(36 degrees)

3. ı know thank but I have to use summation property which is sin(72+18)=sin72.cos18+sin18.cos72 when you plug 2.sin36.cos36 isntead of sin72 but I dont know the rest of soution ı tried

4. Originally Posted by mialkan
ı know thank but I have to use summation property which is sin(72+18)=sin72.cos18+sin18.cos72 when you plug 2.sin36.cos36 isntead of sin72 but I dont know the rest of soution ı tried
$\sin(36^{\text{o}}) = \frac{\sqrt{2(5 - \sqrt{5})}}{4}$.

I don't have time now to type up the derivation - maybe later. Unless someone beats me to it.

5. Originally Posted by mr fantastic
$\sin(36^{\text{o}}) = \frac{\sqrt{2(5 - \sqrt{5})}}{4}$.

I don't have time now to type up the derivation - maybe later. Unless someone beats me to it.
This link should give you enough information to calculate the result.

Alternatively, the result can be got using complex numbers .....

6. Originally Posted by mialkan
Sin36=? without using calculator
Start by setting $\sin36^\circ=\cos54^\circ.$

Since $2\cdot18=36$ & $3\cdot18=54,$ combine double and triple angle formulae for sine and cosine. You'll get a quadratic equation.

7. ## Hi......it's not a problem ...

[QUOTE=mialkan;107293]Sin36=? without using calculator[/QUOTE

For solving this problem.....At first,u consider the value of sin(210 deg)= -1/2,
now we know that 210=36*5;
write the equation....sin(5*36)= -1/2 & then express the equation as a function of sin(36 deg) means sin(5x) in terms of sinx....and then solve the equation...
after solving the equation ....U will get the result.