+0

sin(2arctan(12/5))

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1487
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sin(2arctan(12/5))

Guest Jun 28, 2014

#2
+92254
+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
Sort:

#1
+85958
+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
+92254
+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

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