sin(12^12^14)

$$\small\text{
$
\sin{ ( 12^{12^{14}} \ensurement{^{\circ}} ) } \\
=\sin{ ( 12^{ 168 } \ensurement{^{\circ}} ) } \\
= \sin{ ( 216 \ensurement{^{\circ}} ) } \\
= -0.587785252292
$
}}$$

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({{\left({{\mathtt{12}}}^{{\mathtt{12}}}\right)}}^{{\mathtt{14}}}\right)} = -{\mathtt{0.350\: \!397\: \!680\: \!546}}$$

I like that Heureka.  I would not thought to have used the mod function for this. Thanks ;)

Why is your answer different from Happy's answer?

sin(12^12^14)

Hi Melody,

here is the solution from WolframAlpha:

I think, the argument (12^12)^14 is to big for our calculator. But the mod - function is correct and departs from the argument multiple from 360 degrees.

The formula is  $$\sin(\alpha) = \sin(\alpha \pm n*360\ensurement{^{\circ}} )$$

Thanks heureka,

This post is not just for heureka   

I am still a little confused. Is there a glitch in the calculator?  Why wasn't happy's answer the same?

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{400}}^\circ\right)} = {\mathtt{0.642\: \!787\: \!609\: \!687}}$$

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{400}}{\mathtt{\,-\,}}{\mathtt{360}}\right)} = {\mathtt{0.642\: \!787\: \!609\: \!687}}$$

Okay so why was mod function necessary - was it just that the sine function could not handle an angle that  was so huge?