Find sin (x/2)

Brndo4u · #1 $Old$ November 5th, 2009, 12:22 PM

I have done this problem a few times, still not getting answer the book has.
Could someone solve it? need to use half-angle id's..Thanks.

Sin(x/2), given tan x= 2, with 0<x< pi/2.

e^(i*pi) · #2 $Old$ November 5th, 2009, 01:04 PM

Quote:

Originally Posted by Brndo4u $View Post$

I have done this problem a few times, still not getting answer the book has.
Could someone solve it? need to use half-angle id's..Thanks.

Sin(x/2), given tan x= 2, with 0<x< pi/2.

$sin(\theta) = sin\left(2\,\frac{\theta}{2}\right) = 2sin\left(\frac{\theta}{2}\right)cos\left(\frac{\theta}{2}\right)$

Jameson · #3 $Old$ November 5th, 2009, 01:11 PM

tan(x)=2 gives you enough info to complete the right triangle in quadrant I. Put another way, the tangent is a ratio of two sides of the triangle, so you can use the Pythagorean Theorem to get the 3rd side. Now you just have to plug in the right values into the half angle formula.