If cos x = 4/5 and has its terminal side in the first quadrant, find the exact value of cos x/2.
B balloobear New member Joined Dec 3, 2009 Messages 1 Dec 3, 2009 #1 If cos x = 4/5 and has its terminal side in the first quadrant, find the exact value of cos x/2.
tkhunny Moderator Staff member Joined Apr 12, 2005 Messages 11,339 Dec 3, 2009 #2 Deerive yourself from Double Angle identity. \(\displaystyle cos(2x) = 2 \cdot \cos^{2}(x) - 1\) Make a little modification: \(\displaystyle cos(x) = 2 \cdot \cos^{2}\left(\frac{x}{2}\right) - 1\) Solve for the desired expression.
Deerive yourself from Double Angle identity. \(\displaystyle cos(2x) = 2 \cdot \cos^{2}(x) - 1\) Make a little modification: \(\displaystyle cos(x) = 2 \cdot \cos^{2}\left(\frac{x}{2}\right) - 1\) Solve for the desired expression.
F fasteddie65 Full Member Joined Nov 1, 2008 Messages 360 Dec 11, 2009 #3 Or you could use the identity cos (x/2) = ± ?[(1 + cos x)/2]
tkhunny Moderator Staff member Joined Apr 12, 2005 Messages 11,339 Dec 11, 2009 #4 fasteddie, you're not paying attention. That IS the identity I suggested.