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# sin(12^12^14)

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sin(12^12^14)

Guest Nov 17, 2014

#2
+19207
+13

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

heureka  Nov 18, 2014
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#1
+7188
+8

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

happy7  Nov 17, 2014
#2
+19207
+13

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

heureka  Nov 18, 2014
#3
+92221
0

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

Melody  Nov 18, 2014
#4
+19207
+8

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

heureka  Nov 19, 2014
#5
+92221
0

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?

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

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

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

Melody  Nov 19, 2014

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