HALF ANGLE IDENTITY

[balloobear]

If cos x = 4/5 and has its terminal side in the first quadrant, find the exact value of cos x/2.

 

[tkhunny]

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.

 

[fasteddie65]

Or you could use the identity cos (x/2) = ± ?[(1 + cos x)/2]

 

[tkhunny]

fasteddie, you're not paying attention. That IS the identity I suggested.