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sin(2arctan(12/5))

Guest Jun 28, 2014

Best Answer 

 #2
avatar+93633 
+15

sin(2arctan(12/5))

I always do these by drawing the triangle

$$let\:\theta = atan\:\frac{12}{5}$$

sin(2arctan(12/5))

$$\\Sin(2 atan(12/5))\\
=sin(2\theta)\\
=2sin\theta cos\theta\\
=2\times \frac{12}{13}\times \frac{5}{13}\\
=\frac{120}{169}$$

Melody  Jun 29, 2014
 #1
avatar+89819 
+6

Let's take the "arctan" part first....remember, this will return some angle

arctan(12/5) = 67.38013505196°

So.....2*arctan(12/5) = 2* 67.38013505196°   = 134.76027010392°

And...... sin( 134.76027010392°) = 0.710059171598

 

CPhill  Jun 28, 2014
 #2
avatar+93633 
+15
Best Answer

sin(2arctan(12/5))

I always do these by drawing the triangle

$$let\:\theta = atan\:\frac{12}{5}$$

sin(2arctan(12/5))

$$\\Sin(2 atan(12/5))\\
=sin(2\theta)\\
=2sin\theta cos\theta\\
=2\times \frac{12}{13}\times \frac{5}{13}\\
=\frac{120}{169}$$

Melody  Jun 29, 2014

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