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# How does this? sin

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459
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How does this? =   20 and 70 are in grade

Guest Jun 8, 2015

#2
+94105
+10

Draw a right angled triangles with angles 20 and 70 degrees.

Convince yourself that sin70 = cos 20

Now

$$\\sin^2 20 + sin^2 70 \\\\ =sin^2 20 + cos^2 20 \\\\ =1\\\\\\ remember\; the\; identity\\\\ \boxed{sin^2 \theta + cos^2 \theta=1}$$

Melody  Jun 9, 2015
#1
+14536
+5

$${\underset{\,\,\,\,^{{360^\circ}}}{{sin}}{\left({\mathtt{20}}^\circ\right)}}^{\,{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}\left({\underset{\,\,\,\,^{{360^\circ}}}{{sin}}{\left({\mathtt{70}}^\circ\right)}}^{\,{\mathtt{2}}}\right) = {\mathtt{1}}$$

$${\underset{\,\,\,\,^{{360^\circ}}}{{sin}}{\left({\mathtt{20}}^\circ\right)}}^{\,{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\underset{\,\,\,\,^{{360^\circ}}}{{sin}}{\left({\mathtt{70}}^\circ\right)}}^{\,{\mathtt{2}}} = {\mathtt{1.000\: \!000\: \!000\: \!000\: \!398\: \!8}}$$

#2
+94105
+10

Draw a right angled triangles with angles 20 and 70 degrees.

Convince yourself that sin70 = cos 20

Now

$$\\sin^2 20 + sin^2 70 \\\\ =sin^2 20 + cos^2 20 \\\\ =1\\\\\\ remember\; the\; identity\\\\ \boxed{sin^2 \theta + cos^2 \theta=1}$$

Melody  Jun 9, 2015